he flows of rigid polyvinyl chloride (R-PVC) in co-rotating twin screw extruders with screw mixing elements and regular screw elements were simulated by using the finite element method. The three-dimensional,non-isoth...he flows of rigid polyvinyl chloride (R-PVC) in co-rotating twin screw extruders with screw mixing elements and regular screw elements were simulated by using the finite element method. The three-dimensional,non-isothermal flow fields of R-PVC in the two kinds of screw elements were calculated. The mixing performance of each type of element was studied by the particle tracking analysis method. The results show that the temperature distribution and shear-rate distribution are more uniform in the flow channel with screw mixing elements than in the flow channel with regular screw elements. Screw mixing elements provide better distributive and dispersive mixing performance but worse conveying capacity than regular screw elements.展开更多
In this paper, we present the a posteriori error estimate of two-grid mixed finite element methods by averaging techniques for semilinear elliptic equations. We first propose the two-grid algorithms to linearize the m...In this paper, we present the a posteriori error estimate of two-grid mixed finite element methods by averaging techniques for semilinear elliptic equations. We first propose the two-grid algorithms to linearize the mixed method equations. Then, the averaging technique is used to construct the a posteriori error estimates of the two-grid mixed finite element method and theoretical analysis are given for the error estimators. Finally, we give some numerical examples to verify the reliability and efficiency of the a posteriori error estimator.展开更多
A highly efficient H1-Galerkin mixed finite element method(MFEM) is presented with linear triangular element for the parabolic integro-differential equation.Firstly, some new results about the integral estimation and ...A highly efficient H1-Galerkin mixed finite element method(MFEM) is presented with linear triangular element for the parabolic integro-differential equation.Firstly, some new results about the integral estimation and asymptotic expansions are studied. Then, the superconvergence of order O(h2) for both the original variable u in H1(π) norm and the flux p =u in H(div,π) norm is derived through the interpolation post processing technique. Furthermore, with the help of the asymptotic expansions and a suitable auxiliary problem, the extrapolation solutions with accuracy O(h3) are obtained for the above two variables. Finally, some numerical results are provided to confirm validity of the theoretical analysis and excellent performance of the proposed method.展开更多
Mixed element formats of any order based on bubble functions for the stationary Stokes problem are derived in triangular and tetrahedral meshes and the convergence of these formats are proved.
In this study, we employ mixed finite element(MFE) method, two local Gauss integrals, and parameter-free to establish a stabilized MFE formulation for the non-stationary incompressible Boussinesq equations. We also pr...In this study, we employ mixed finite element(MFE) method, two local Gauss integrals, and parameter-free to establish a stabilized MFE formulation for the non-stationary incompressible Boussinesq equations. We also provide the theoretical analysis of the existence,uniqueness, stability, and convergence of the stabilized MFE solutions for the stabilized MFE formulation.展开更多
The penalty and hybrid methods are being much used in dealing with the general incompatible element. With the penalty method convergence can always be assured, but comparatively speaking its accuracy is lower; and the...The penalty and hybrid methods are being much used in dealing with the general incompatible element. With the penalty method convergence can always be assured, but comparatively speaking its accuracy is lower; and the condition number and sparsity are not so good. With the hybrid method, convergence can be assured only when the rank condition is satisfied. So the construction of the element isextremely limited. This paper presents the mixed hybrid penalty element method, which combines the two methods together.And it is proved theoretically that this new method is convergent, and it has the same accuracy, condition number and sparsity as the compatible element.That is to say, they are optimal to each other. Finally, a new triangle element for plate bending with nine freedom degrees is constructed with this method (three degrees of freedom are given on each corner——one displacement and two rotations), the calculating formula of the element stiffness matrix is almost the same as that of the old展开更多
<span style="font-family:Verdana;">In this paper, for the initial and boundary value problem of beams with</span> <span style="font-family:Verdana;">structural damping, by introdu...<span style="font-family:Verdana;">In this paper, for the initial and boundary value problem of beams with</span> <span style="font-family:Verdana;">structural damping, by introducing intermediate variables, the original </span><span style="font-family:Verdana;">fourth-order problem is transformed into second-order partial differential equations, and the mixed finite volume element scheme is constructed, and the existence, uniqueness and convergence of the scheme are analyzed</span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">.</span></span></span><span><span><span style="font-family:Verdana;"> Numerical examples are provided to confirm the theoretical results. In the end, we test the value of <em>δ</em></span><span style="font-family:Verdana;"> to observe its influence on the model.</span></span></span>展开更多
The warping may become an important factor for the precise transverse vibrations of curved beams.Thus,the first aim of this study is to specify the structural design parameters where the influence of cross-sectional w...The warping may become an important factor for the precise transverse vibrations of curved beams.Thus,the first aim of this study is to specify the structural design parameters where the influence of cross-sectional warping becomes great and the first-order shear deformation theory lacks the precision necessary.The outof-plane vibrations of the first-order shear deformation theory are compared with the warping-included vibrations as the curvature and/or thickness increase for symmetric and asymmetric transversely-functionally graded(TFG)curved beams.The second aim is to determine the influence of design parameters on the vibrations.The circular/exact elliptical beams are formed via curved mixed finite elements(MFEs)based on the exact curvature and length.The stress-free conditions are satisfied on three-dimensional(3D)constitutive equations.The variation of functionally graded(FG)material constituents is considered based on the power-law dependence.The cross-sectional warping deformations are defined over a displacement-type FE formulation.The warping-included MFEs(W-MFEs)provide satisfactory 3D structural characteristics with smaller degrees of freedom(DOFs)compared with the brick FEs.The Newmark method is used for the forced vibrations.展开更多
In this paper,we consider the initial-boundary value problem(IBVP)for the micropolar Naviers-Stokes equations(MNSE)and analyze a first order fully discrete mixed finite element scheme.We first establish some regularit...In this paper,we consider the initial-boundary value problem(IBVP)for the micropolar Naviers-Stokes equations(MNSE)and analyze a first order fully discrete mixed finite element scheme.We first establish some regularity results for the solution of MNSE,which seem to be not available in the literature.Next,we study a semi-implicit time-discrete scheme for the MNSE and prove L2-H1 error estimates for the time discrete solution.Furthermore,certain regularity results for the time discrete solution are establishes rigorously.Based on these regularity results,we prove the unconditional L2-H1 error estimates for the finite element solution of MNSE.Finally,some numerical examples are carried out to demonstrate both accuracy and efficiency of the fully discrete finite element scheme.展开更多
In this paper,a two-grid mixed finite element method(MFEM)of implicit Backward Euler(BE)formula is presented for the fourth order time-dependent singularly perturbed Bi-wave problem for d-wave superconductors by the n...In this paper,a two-grid mixed finite element method(MFEM)of implicit Backward Euler(BE)formula is presented for the fourth order time-dependent singularly perturbed Bi-wave problem for d-wave superconductors by the nonconforming EQ_(1)^(rot) element.In this approach,the original nonlinear system is solved on the coarse mesh through the Newton iteration method,and then the linear system is computed on the fine mesh with Taylor’s expansion.Based on the high accuracy results of the chosen element,the uniform superclose and superconvergent estimates in the broken H^(1)-norm are derived,which are independent of the negative powers of the perturbation parameter appeared in the considered problem.Numerical results illustrate that the computing cost of the proposed two-grid method is much less than that of the conventional Galerkin MFEM without loss of accuracy.展开更多
The mathematical model of a semiconductor device is governed by a system of quasi-linear partial differential equations.The electric potential equation is approximated by a mixed finite element method,and the concentr...The mathematical model of a semiconductor device is governed by a system of quasi-linear partial differential equations.The electric potential equation is approximated by a mixed finite element method,and the concentration equations are approximated by a standard Galerkin method.We estimate the error of the numerical solutions in the sense of the Lqnorm.To linearize the full discrete scheme of the problem,we present an efficient two-grid method based on the idea of Newton iteration.The main procedures are to solve the small scaled nonlinear equations on the coarse grid and then deal with the linear equations on the fine grid.Error estimation for the two-grid solutions is analyzed in detail.It is shown that this method still achieves asymptotically optimal approximations as long as a mesh size satisfies H=O(h^1/2).Numerical experiments are given to illustrate the efficiency of the two-grid method.展开更多
In this paper, a nonconforming triangular mixed finite element scheme with second order convergence behavior is proposed for the stationary Navier-Stokes equations.The new nonconforming triangular element is taken as ...In this paper, a nonconforming triangular mixed finite element scheme with second order convergence behavior is proposed for the stationary Navier-Stokes equations.The new nonconforming triangular element is taken as approximation space for the velocity and the linear element for the pressure. The convergence analysis is presented and optimal error estimates of both broken H^1-norm and L^2-norm for velocity as well as the L^2-norm for the pressure are derived.展开更多
Mixed finite element methods are considered for a ferrofluid flow model with magnetization paralleled to the magnetic field.The ferrofluid model is a coupled system of the Maxwell equations and the incompressible Navi...Mixed finite element methods are considered for a ferrofluid flow model with magnetization paralleled to the magnetic field.The ferrofluid model is a coupled system of the Maxwell equations and the incompressible Navier-Stokes equations.By skillfully introducing some new variables,the model is rewritten as several decoupled subsystems that can be solved independently.Mixed finite element formulations are given to discretize the decoupled systems with proper finite element spaces.Existence and uniqueness of the mixed finite element solutions are shown,and optimal order error estimates are obtained under some reasonable assumptions.Numerical experiments confirm the theoretical results.展开更多
In this article,we propose a new finite element spaceΛh for the expanded mixed finite element method(EMFEM)for second-order elliptic problems to guarantee its computing capability and reduce the computation cost.The ...In this article,we propose a new finite element spaceΛh for the expanded mixed finite element method(EMFEM)for second-order elliptic problems to guarantee its computing capability and reduce the computation cost.The new finite element spaceΛh is designed in such a way that the strong requirement V h⊂Λh in[9]is weakened to{v h∈V h;d i v v h=0}⊂Λh so that it needs fewer degrees of freedom than its classical counterpart.Furthermore,the newΛh coupled with the Raviart-Thomas space satisfies the inf-sup condition,which is crucial to the computation of mixed methods for its close relation to the behavior of the smallest nonzero eigenvalue of the stiff matrix,and thus the existence,uniqueness and optimal approximate capability of the EMFEM solution are proved for rectangular partitions in R d,d=2,3 and for triangular partitions in R 2.Also,the solvability of the EMFEM for triangular partition in R 3 can be directly proved without the inf-sup condition.Numerical experiments are conducted to confirm these theoretical findings.展开更多
In this paper,we investigate a priori error estimates for the quadratic optimal control problems governed by semilinear elliptic partial differential equations using higher order triangular mixed finite element method...In this paper,we investigate a priori error estimates for the quadratic optimal control problems governed by semilinear elliptic partial differential equations using higher order triangular mixed finite element methods.The state and the co-state are approximated by the order k Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise polynomials of order k(k≥0).A priori error estimates for the mixed finite element approximation of semilinear control problems are obtained.Finally,we present some numerical examples which confirm our theoretical results.展开更多
In this paper,a general method to derive asymptotic error expansion formulas for the mixed finite element approximations of the Maxwell eigenvalue problem is established.Abstract lemmas for the error of the eigenvalu...In this paper,a general method to derive asymptotic error expansion formulas for the mixed finite element approximations of the Maxwell eigenvalue problem is established.Abstract lemmas for the error of the eigenvalue approximations are obtained.Based on the asymptotic error expansion formulas,the Richardson extrapolation method is employed to improve the accuracy of the approximations for the eigenvalues of the Maxwell system from O(h2)to O(h4)when applying the lowest order Nédélec mixed finite element and a nonconforming mixed finite element.To our best knowledge,this is the first superconvergence result of the Maxwell eigenvalue problem by the extrapolation of the mixed finite element approximation.Numerical experiments are provided to demonstrate the theoretical results.展开更多
In this paper,we investigate a priori and a posteriori error estimates of fully discrete H^(1)-Galerkin mixed finite element methods for parabolic optimal control prob-lems.The state variables and co-state variables a...In this paper,we investigate a priori and a posteriori error estimates of fully discrete H^(1)-Galerkin mixed finite element methods for parabolic optimal control prob-lems.The state variables and co-state variables are approximated by the lowest order Raviart-Thomas mixed finite element and linear finite element,and the control vari-able is approximated by piecewise constant functions.The time discretization of the state and co-state are based on finite difference methods.First,we derive a priori error estimates for the control variable,the state variables and the adjoint state variables.Second,by use of energy approach,we derive a posteriori error estimates for optimal control problems,assuming that only the underlying mesh is static.A numerical example is presented to verify the theoretical results on a priori error estimates.展开更多
This paper deals with Raviart-Thomas element (Q2,1 × Q1,2 - Q1 element).Apart from its global superconvergence property of fourth order, we prove that apostprocessed extrapolation can globally increased the accur...This paper deals with Raviart-Thomas element (Q2,1 × Q1,2 - Q1 element).Apart from its global superconvergence property of fourth order, we prove that apostprocessed extrapolation can globally increased the accuracy by fifth order.展开更多
A numerical method based on the explicit two-step method in time direction and the mixed finite element method in spatial direction is presented for the symmetric regularized long wave(SRLW)equation.The optimal a prio...A numerical method based on the explicit two-step method in time direction and the mixed finite element method in spatial direction is presented for the symmetric regularized long wave(SRLW)equation.The optimal a priori error estimates(O((∆t)^(2)+h^(m+1)+h^(k+1)))for fully discrete explicit two-step mixed scheme are derived.Moreover,a numerical example is provided to confirm our theoretical results.展开更多
文摘he flows of rigid polyvinyl chloride (R-PVC) in co-rotating twin screw extruders with screw mixing elements and regular screw elements were simulated by using the finite element method. The three-dimensional,non-isothermal flow fields of R-PVC in the two kinds of screw elements were calculated. The mixing performance of each type of element was studied by the particle tracking analysis method. The results show that the temperature distribution and shear-rate distribution are more uniform in the flow channel with screw mixing elements than in the flow channel with regular screw elements. Screw mixing elements provide better distributive and dispersive mixing performance but worse conveying capacity than regular screw elements.
文摘In this paper, we present the a posteriori error estimate of two-grid mixed finite element methods by averaging techniques for semilinear elliptic equations. We first propose the two-grid algorithms to linearize the mixed method equations. Then, the averaging technique is used to construct the a posteriori error estimates of the two-grid mixed finite element method and theoretical analysis are given for the error estimators. Finally, we give some numerical examples to verify the reliability and efficiency of the a posteriori error estimator.
基金Project supported by the National Natural Science Foundation of China(Nos.10971203,11271340,and 11101381)the Specialized Research Fund for the Doctoral Program of Higher Education(No.20094101110006)
文摘A highly efficient H1-Galerkin mixed finite element method(MFEM) is presented with linear triangular element for the parabolic integro-differential equation.Firstly, some new results about the integral estimation and asymptotic expansions are studied. Then, the superconvergence of order O(h2) for both the original variable u in H1(π) norm and the flux p =u in H(div,π) norm is derived through the interpolation post processing technique. Furthermore, with the help of the asymptotic expansions and a suitable auxiliary problem, the extrapolation solutions with accuracy O(h3) are obtained for the above two variables. Finally, some numerical results are provided to confirm validity of the theoretical analysis and excellent performance of the proposed method.
基金Supported by National Natural Science Foundation of China(11371331)Supported by the Natural Science Foundation of Education Department of Henan Province(14B110018)
文摘Mixed element formats of any order based on bubble functions for the stationary Stokes problem are derived in triangular and tetrahedral meshes and the convergence of these formats are proved.
基金supported by the National Science Foundation of China(11271127)Science Research Project of Guizhou Province Education Department(QJHKYZ[2013]207)
文摘In this study, we employ mixed finite element(MFE) method, two local Gauss integrals, and parameter-free to establish a stabilized MFE formulation for the non-stationary incompressible Boussinesq equations. We also provide the theoretical analysis of the existence,uniqueness, stability, and convergence of the stabilized MFE solutions for the stabilized MFE formulation.
文摘The penalty and hybrid methods are being much used in dealing with the general incompatible element. With the penalty method convergence can always be assured, but comparatively speaking its accuracy is lower; and the condition number and sparsity are not so good. With the hybrid method, convergence can be assured only when the rank condition is satisfied. So the construction of the element isextremely limited. This paper presents the mixed hybrid penalty element method, which combines the two methods together.And it is proved theoretically that this new method is convergent, and it has the same accuracy, condition number and sparsity as the compatible element.That is to say, they are optimal to each other. Finally, a new triangle element for plate bending with nine freedom degrees is constructed with this method (three degrees of freedom are given on each corner——one displacement and two rotations), the calculating formula of the element stiffness matrix is almost the same as that of the old
文摘<span style="font-family:Verdana;">In this paper, for the initial and boundary value problem of beams with</span> <span style="font-family:Verdana;">structural damping, by introducing intermediate variables, the original </span><span style="font-family:Verdana;">fourth-order problem is transformed into second-order partial differential equations, and the mixed finite volume element scheme is constructed, and the existence, uniqueness and convergence of the scheme are analyzed</span><span style="font-family:Verdana;"><span style="font-family:Verdana;"><span style="font-family:Verdana;">.</span></span></span><span><span><span style="font-family:Verdana;"> Numerical examples are provided to confirm the theoretical results. In the end, we test the value of <em>δ</em></span><span style="font-family:Verdana;"> to observe its influence on the model.</span></span></span>
基金Project supported by the Scientific and Technological Research Council of Turkey(TUBITAK)via 2209-A Programme。
文摘The warping may become an important factor for the precise transverse vibrations of curved beams.Thus,the first aim of this study is to specify the structural design parameters where the influence of cross-sectional warping becomes great and the first-order shear deformation theory lacks the precision necessary.The outof-plane vibrations of the first-order shear deformation theory are compared with the warping-included vibrations as the curvature and/or thickness increase for symmetric and asymmetric transversely-functionally graded(TFG)curved beams.The second aim is to determine the influence of design parameters on the vibrations.The circular/exact elliptical beams are formed via curved mixed finite elements(MFEs)based on the exact curvature and length.The stress-free conditions are satisfied on three-dimensional(3D)constitutive equations.The variation of functionally graded(FG)material constituents is considered based on the power-law dependence.The cross-sectional warping deformations are defined over a displacement-type FE formulation.The warping-included MFEs(W-MFEs)provide satisfactory 3D structural characteristics with smaller degrees of freedom(DOFs)compared with the brick FEs.The Newmark method is used for the forced vibrations.
基金supported by the National Natural Science Foundation of China(Grant Nos.11871467,11471329).
文摘In this paper,we consider the initial-boundary value problem(IBVP)for the micropolar Naviers-Stokes equations(MNSE)and analyze a first order fully discrete mixed finite element scheme.We first establish some regularity results for the solution of MNSE,which seem to be not available in the literature.Next,we study a semi-implicit time-discrete scheme for the MNSE and prove L2-H1 error estimates for the time discrete solution.Furthermore,certain regularity results for the time discrete solution are establishes rigorously.Based on these regularity results,we prove the unconditional L2-H1 error estimates for the finite element solution of MNSE.Finally,some numerical examples are carried out to demonstrate both accuracy and efficiency of the fully discrete finite element scheme.
基金supported by the National Natural Science Foundation of China(Grant Nos.12201640,12071443).
文摘In this paper,a two-grid mixed finite element method(MFEM)of implicit Backward Euler(BE)formula is presented for the fourth order time-dependent singularly perturbed Bi-wave problem for d-wave superconductors by the nonconforming EQ_(1)^(rot) element.In this approach,the original nonlinear system is solved on the coarse mesh through the Newton iteration method,and then the linear system is computed on the fine mesh with Taylor’s expansion.Based on the high accuracy results of the chosen element,the uniform superclose and superconvergent estimates in the broken H^(1)-norm are derived,which are independent of the negative powers of the perturbation parameter appeared in the considered problem.Numerical results illustrate that the computing cost of the proposed two-grid method is much less than that of the conventional Galerkin MFEM without loss of accuracy.
基金Project supported by the State Key Program of National Natural Science Foundation of China(No.11931003)the National Natural Science Foundation of China(Nos.41974133,11671157,11971410)。
文摘The mathematical model of a semiconductor device is governed by a system of quasi-linear partial differential equations.The electric potential equation is approximated by a mixed finite element method,and the concentration equations are approximated by a standard Galerkin method.We estimate the error of the numerical solutions in the sense of the Lqnorm.To linearize the full discrete scheme of the problem,we present an efficient two-grid method based on the idea of Newton iteration.The main procedures are to solve the small scaled nonlinear equations on the coarse grid and then deal with the linear equations on the fine grid.Error estimation for the two-grid solutions is analyzed in detail.It is shown that this method still achieves asymptotically optimal approximations as long as a mesh size satisfies H=O(h^1/2).Numerical experiments are given to illustrate the efficiency of the two-grid method.
基金Supported by the National Natural Science Foundation of China(11271340,116713697)Supported by Henan Natural Science Foundation of China(132300410376)
文摘In this paper, a nonconforming triangular mixed finite element scheme with second order convergence behavior is proposed for the stationary Navier-Stokes equations.The new nonconforming triangular element is taken as approximation space for the velocity and the linear element for the pressure. The convergence analysis is presented and optimal error estimates of both broken H^1-norm and L^2-norm for velocity as well as the L^2-norm for the pressure are derived.
基金supported by the National Natural Science Foundation of China(Grant Nos.11971094,12171340).
文摘Mixed finite element methods are considered for a ferrofluid flow model with magnetization paralleled to the magnetic field.The ferrofluid model is a coupled system of the Maxwell equations and the incompressible Navier-Stokes equations.By skillfully introducing some new variables,the model is rewritten as several decoupled subsystems that can be solved independently.Mixed finite element formulations are given to discretize the decoupled systems with proper finite element spaces.Existence and uniqueness of the mixed finite element solutions are shown,and optimal order error estimates are obtained under some reasonable assumptions.Numerical experiments confirm the theoretical results.
基金supported by NSF of China grant 11971276H.Chen was supported by NSF of China grants 12171287,10971254 and 11471196+1 种基金H.Wang was supported by the ARO MURI Grant W911NF-15-1-0562by the National Science Foundation under Grant DMS-2012291.
文摘In this article,we propose a new finite element spaceΛh for the expanded mixed finite element method(EMFEM)for second-order elliptic problems to guarantee its computing capability and reduce the computation cost.The new finite element spaceΛh is designed in such a way that the strong requirement V h⊂Λh in[9]is weakened to{v h∈V h;d i v v h=0}⊂Λh so that it needs fewer degrees of freedom than its classical counterpart.Furthermore,the newΛh coupled with the Raviart-Thomas space satisfies the inf-sup condition,which is crucial to the computation of mixed methods for its close relation to the behavior of the smallest nonzero eigenvalue of the stiff matrix,and thus the existence,uniqueness and optimal approximate capability of the EMFEM solution are proved for rectangular partitions in R d,d=2,3 and for triangular partitions in R 2.Also,the solvability of the EMFEM for triangular partition in R 3 can be directly proved without the inf-sup condition.Numerical experiments are conducted to confirm these theoretical findings.
基金supported by the Foundation for Talent Introduction of Guangdong Provincial Universities and CollegesPearl River Scholar Funded Scheme(2008)National Science Foundation of China(10971074).
文摘In this paper,we investigate a priori error estimates for the quadratic optimal control problems governed by semilinear elliptic partial differential equations using higher order triangular mixed finite element methods.The state and the co-state are approximated by the order k Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise polynomials of order k(k≥0).A priori error estimates for the mixed finite element approximation of semilinear control problems are obtained.Finally,we present some numerical examples which confirm our theoretical results.
基金The first author was supported in part by NSFF P.R.China NO.10971203。
文摘In this paper,a general method to derive asymptotic error expansion formulas for the mixed finite element approximations of the Maxwell eigenvalue problem is established.Abstract lemmas for the error of the eigenvalue approximations are obtained.Based on the asymptotic error expansion formulas,the Richardson extrapolation method is employed to improve the accuracy of the approximations for the eigenvalues of the Maxwell system from O(h2)to O(h4)when applying the lowest order Nédélec mixed finite element and a nonconforming mixed finite element.To our best knowledge,this is the first superconvergence result of the Maxwell eigenvalue problem by the extrapolation of the mixed finite element approximation.Numerical experiments are provided to demonstrate the theoretical results.
基金This work was supported by National Natural Science Foundation of China(11601014,11626037,11526036)China Postdoctoral Science Foundation(2016M 601359)+4 种基金Scientific and Technological Developing Scheme of Jilin Province(20160520108 JH,20170101037JC)Science and Technology Research Project of Jilin Provincial Depart-ment of Education(201646)Special Funding for Promotion of Young Teachers of Beihua University,Natural Science Foundation of Hunan Province(14JJ3135)the Youth Project of Hunan Provincial Education Department(15B096)the construct program of the key discipline in Hunan University of Science and Engineering.
文摘In this paper,we investigate a priori and a posteriori error estimates of fully discrete H^(1)-Galerkin mixed finite element methods for parabolic optimal control prob-lems.The state variables and co-state variables are approximated by the lowest order Raviart-Thomas mixed finite element and linear finite element,and the control vari-able is approximated by piecewise constant functions.The time discretization of the state and co-state are based on finite difference methods.First,we derive a priori error estimates for the control variable,the state variables and the adjoint state variables.Second,by use of energy approach,we derive a posteriori error estimates for optimal control problems,assuming that only the underlying mesh is static.A numerical example is presented to verify the theoretical results on a priori error estimates.
文摘This paper deals with Raviart-Thomas element (Q2,1 × Q1,2 - Q1 element).Apart from its global superconvergence property of fourth order, we prove that apostprocessed extrapolation can globally increased the accuracy by fifth order.
基金supported by the National Natural Science Fund of China(11061021,11301258 and 11361035)the Scientific Research Projection of Higher Schools of Inner Mongolia(NJZZ12011 and NJZY13199)+1 种基金the Natural Science Fund of Inner Mongolia Province(2012MS0106 and 2012MS0108)the Program of Higher-level talents of Inner Mongolia University(125119).
文摘A numerical method based on the explicit two-step method in time direction and the mixed finite element method in spatial direction is presented for the symmetric regularized long wave(SRLW)equation.The optimal a priori error estimates(O((∆t)^(2)+h^(m+1)+h^(k+1)))for fully discrete explicit two-step mixed scheme are derived.Moreover,a numerical example is provided to confirm our theoretical results.