This paper considers the regularity of solutions to mixed boundary value problems in small-angle regions for elliptic equations. By constructing a specific barrier function, we proved that under the assumption of suff...This paper considers the regularity of solutions to mixed boundary value problems in small-angle regions for elliptic equations. By constructing a specific barrier function, we proved that under the assumption of sufficient regularity of boundary conditions and coefficients, as long as the angle is sufficiently small, the regularity of the solution to the mixed boundary value problem of the second-order elliptic equation can reach any order.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
An H^1-Galerkin mixed finite element method is discussed for a class of second order SchrSdinger equation. Optimal error estimates of semidiscrete schemes are derived for problems in one space dimension. At the same t...An H^1-Galerkin mixed finite element method is discussed for a class of second order SchrSdinger equation. Optimal error estimates of semidiscrete schemes are derived for problems in one space dimension. At the same time, optimal error estimates are derived for fully discrete schemes. And it is showed that the H1-Galerkin mixed finite element approximations have the same rate of convergence as in the classical mixed finite element methods without requiring the LBB consistency condition.展开更多
The existence, uniqueness and non-symmetric iterative approximation of solutions for a class of systems of mixed monotone operator equations are discussed. As an application, we utilize, the results presented in this ...The existence, uniqueness and non-symmetric iterative approximation of solutions for a class of systems of mixed monotone operator equations are discussed. As an application, we utilize, the results presented in this paper to study the existence and uniqueness problems of common solutions for a class of systems of functional equations arising in dynamic programming of multistage decision processes and a class of systems of nonlinear integral equation. The results obtained in this paper not only answer an open question suggested in [3] but also generalize the corresponding results of [1],[2].展开更多
In this article, a new stable nonconforming mixed finite element scheme is proposed for the stationary Navier-Stokes equations, in which a new low order Crouzeix- Raviart type nonconforming rectangular element is take...In this article, a new stable nonconforming mixed finite element scheme is proposed for the stationary Navier-Stokes equations, in which a new low order Crouzeix- Raviart type nonconforming rectangular element is taken for approximating space for the velocity and the piecewise constant element for the pressure. The optimal order error estimates for the approximation of both the velocity and the pressure in L2-norm are established, as well as one in broken H1-norm for the velocity. Numerical experiments are given which are consistent with our theoretical analysis.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 ...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(h^2) for both the original variable u in H1 (Ω) norm and the flux p = u in H(div, Ω) 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(h^3) 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
The purpose of this paper is to investigate the convergence of the mixed finite element method for the initial-boundary value problem for the Sobolev equation Ut-div{aut + b1 u} = f based on the Raviart-Thomas space ...The purpose of this paper is to investigate the convergence of the mixed finite element method for the initial-boundary value problem for the Sobolev equation Ut-div{aut + b1 u} = f based on the Raviart-Thomas space Vh × Wh H(div; × L2(). Optimal order estimates are obtained for the approximation of u, ut, the associated velocity p and divp respectively in L(0,T;L2()), L(0,T;L2()), L(0,T;L2()2), and L2(0, T; L2()). Quasi-optimal order estimates are obtained for the approximations of u, ut in L(0, T; L()) and p in L(0,T; L()2).展开更多
The mixed covolume method for the regularized long wave equation is devel- oped and studied. By introducing a transfer operator γh, which maps the trial function space into the test function space, and combining the ...The mixed covolume method for the regularized long wave equation is devel- oped and studied. By introducing a transfer operator γh, which maps the trial function space into the test function space, and combining the mixed finite element with the finite volume method, the nonlinear and linear Euler fully discrete mixed covolume schemes are constructed, and the existence and uniqueness of the solutions are proved. The optimal error estimates for these schemes are obtained. Finally, a numerical example is provided to examine the efficiency of the proposed schemes.展开更多
In this paper, we study the mixed element method for Sobolev equations. A time-discretization procedure is presented and analysed and the optimal order error estimates are derived.For convenience in practical computat...In this paper, we study the mixed element method for Sobolev equations. A time-discretization procedure is presented and analysed and the optimal order error estimates are derived.For convenience in practical computation, an alternating-direction iterative scheme of the mixed fi-nite element method is formulated and its stability and converbence are proved for the linear prob-lem. A numerical example is provided at the end of this paper.展开更多
An H1-Galerkin expanded mixed finite element method is discussed for a class of second order semi-linear hyperbolic wave equations. By using the mixed formulation, we can get the optimal approximation for three variab...An H1-Galerkin expanded mixed finite element method is discussed for a class of second order semi-linear hyperbolic wave equations. By using the mixed formulation, we can get the optimal approximation for three variables: the scalar unknown, its gradient and its flux(coefficient times the gradient), simultaneously. We also prove the existence and uniqueness of semi-discrete solution. Finally, we obtain some numerical results to illustrate the efficiency of the method.展开更多
This paper is devoted to the Tricomi problem for a mixed type equation of second order. The coeffcients are assumed to be discontinuous on the line where the type is changed. The unique existence of the solution to th...This paper is devoted to the Tricomi problem for a mixed type equation of second order. The coeffcients are assumed to be discontinuous on the line where the type is changed. The unique existence of the solution to the problem is proved if the domain is small enough. Correspondingly, some estimates on the solution is also established.展开更多
The present article deals with oblique derivative problems for some nonlinear mixed equations with parabolic degeneracy, which include the Tricomi problem as a special case. First, the formulation of the problems for ...The present article deals with oblique derivative problems for some nonlinear mixed equations with parabolic degeneracy, which include the Tricomi problem as a special case. First, the formulation of the problems for the equations is given; next, the representation and estimates of solutions for the above problems are obtained; finally, the existence of solutions for the problems is proved by the successive iteration and the compactness principle of solutions of the problems. In this article, the author uses the complex method, namely, the complex functions in the elliptic domain and the hyperbolic complex functions in hyperbolic domain are used.展开更多
Two new convection-dominated are derived under the approximate solutions least-squares mixed finite element procedures are formulated for solving Sobolev equations. Optimal H(div;Ω)×H1(Ω) norms error estima...Two new convection-dominated are derived under the approximate solutions least-squares mixed finite element procedures are formulated for solving Sobolev equations. Optimal H(div;Ω)×H1(Ω) norms error estimates standard mixed finite spaces. Moreover, these two schemes provide the with first-order and second-order accuracy in time increment, respectively.展开更多
The objective of this paper is to study the oscillatory and asymptotic properties of the mixed type third order neutral difference equation of the form△(an△^2(xn+bnxn-τ1+cnxn+τ2))+qnx^βn+1-σ1+pnx^^βn...The objective of this paper is to study the oscillatory and asymptotic properties of the mixed type third order neutral difference equation of the form△(an△^2(xn+bnxn-τ1+cnxn+τ2))+qnx^βn+1-σ1+pnx^^βn+1+σ2=0,where (an), (bn}, (cn}, (qn} and (pn} are positive real sequences, β is a ratio of odd positive integers, τ1, τ2, and σ2 are positive integers. We establish some sufficient conditions which ensure that all solutions are either oscillatory or converges to zero. Some examples are presented to illustrate the main results.展开更多
A mixed time discontinuous space-time finite element scheme for secondorder convection diffusion problems is constructed and analyzed. Order of the equation is lowered by the mixed finite element method. The low order...A mixed time discontinuous space-time finite element scheme for secondorder convection diffusion problems is constructed and analyzed. Order of the equation is lowered by the mixed finite element method. The low order equation is discretized with a space-time finite element method, continuous in space but discontinuous in time. Stability, existence, uniqueness and convergence of the approximate solutions are proved. Numerical results are presented to illustrate efficiency of the proposed method.展开更多
The existence and multiplicity of positive solutions are studied for a class of quasi- linear elliptic equations involving Sobolev critical exponents with mixed Dirichlet-Neumann boundary conditions by the variational...The existence and multiplicity of positive solutions are studied for a class of quasi- linear elliptic equations involving Sobolev critical exponents with mixed Dirichlet-Neumann boundary conditions by the variational methods and some analytical techniques.展开更多
A new mixed scheme which combines the variation of constants and the H1-Galerkin mixed finite element method is constructed for nonlinear Sobolev equation with nonlinear con- vection term. Optimal error estimates are ...A new mixed scheme which combines the variation of constants and the H1-Galerkin mixed finite element method is constructed for nonlinear Sobolev equation with nonlinear con- vection term. Optimal error estimates are derived for both semidiscrete and fully discrete schemes. Finally, some numerical results are given to confirm the theoretical analysis of the proposed method.展开更多
Through the paper, a general solution of a mixed type functional equation in fuzzy Banach space is obtained and by using the fixed point method a generalized Hyers-Ulam-Rassias stability of the mixed type functional e...Through the paper, a general solution of a mixed type functional equation in fuzzy Banach space is obtained and by using the fixed point method a generalized Hyers-Ulam-Rassias stability of the mixed type functional equation in fuzzy Banach space is proved.展开更多
In this paper, we obtained some sufficient conditions for the oscillation of all solutions of the second order neutral differential equation of the form where , and . Examples are provided to illustrate the main results.
A continuous time and mixed state branching process is constructed by a scaling limit theorem of two-type Galton-Watson processes.The process can also be obtained by the pathwise unique solution to a stochastic equati...A continuous time and mixed state branching process is constructed by a scaling limit theorem of two-type Galton-Watson processes.The process can also be obtained by the pathwise unique solution to a stochastic equation system.From the stochastic equation system we derive the distribution of local jumps and give the exponential ergodicity in Wasserstein-type distances of the transition semigroup.Meanwhile,we study immigration structures associated with the process and prove the existence of the stationary distribution of the process with immigration.展开更多
文摘This paper considers the regularity of solutions to mixed boundary value problems in small-angle regions for elliptic equations. By constructing a specific barrier function, we proved that under the assumption of sufficient regularity of boundary conditions and coefficients, as long as the angle is sufficiently small, the regularity of the solution to the mixed boundary value problem of the second-order elliptic equation can reach any order.
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Supported by the National Natural Science Foundation of China (10601022)Natural Science Foundation of Inner Mongolia Autonomous Region (200607010106)Youth Science Foundation of Inner Mongolia University(ND0702)
文摘An H^1-Galerkin mixed finite element method is discussed for a class of second order SchrSdinger equation. Optimal error estimates of semidiscrete schemes are derived for problems in one space dimension. At the same time, optimal error estimates are derived for fully discrete schemes. And it is showed that the H1-Galerkin mixed finite element approximations have the same rate of convergence as in the classical mixed finite element methods without requiring the LBB consistency condition.
基金Supported by National Natural Science Foundation of China
文摘The existence, uniqueness and non-symmetric iterative approximation of solutions for a class of systems of mixed monotone operator equations are discussed. As an application, we utilize, the results presented in this paper to study the existence and uniqueness problems of common solutions for a class of systems of functional equations arising in dynamic programming of multistage decision processes and a class of systems of nonlinear integral equation. The results obtained in this paper not only answer an open question suggested in [3] but also generalize the corresponding results of [1],[2].
文摘In this article, a new stable nonconforming mixed finite element scheme is proposed for the stationary Navier-Stokes equations, in which a new low order Crouzeix- Raviart type nonconforming rectangular element is taken for approximating space for the velocity and the piecewise constant element for the pressure. The optimal order error estimates for the approximation of both the velocity and the pressure in L2-norm are established, as well as one in broken H1-norm for the velocity. Numerical experiments are given which are consistent with our theoretical analysis.
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(h^2) for both the original variable u in H1 (Ω) norm and the flux p = u in H(div, Ω) 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(h^3) 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.
文摘The purpose of this paper is to investigate the convergence of the mixed finite element method for the initial-boundary value problem for the Sobolev equation Ut-div{aut + b1 u} = f based on the Raviart-Thomas space Vh × Wh H(div; × L2(). Optimal order estimates are obtained for the approximation of u, ut, the associated velocity p and divp respectively in L(0,T;L2()), L(0,T;L2()), L(0,T;L2()2), and L2(0, T; L2()). Quasi-optimal order estimates are obtained for the approximations of u, ut in L(0, T; L()) and p in L(0,T; L()2).
基金supported by the National Natural Science Fundation of China (No. 11061021)the Science Research of Inner Mongolia Advanced Education (Nos. NJ10006, NJ10016, and NJZZ12011)the National Science Foundation of Inner Mongolia (Nos. 2011BS0102 and 2012MS0106)
文摘The mixed covolume method for the regularized long wave equation is devel- oped and studied. By introducing a transfer operator γh, which maps the trial function space into the test function space, and combining the mixed finite element with the finite volume method, the nonlinear and linear Euler fully discrete mixed covolume schemes are constructed, and the existence and uniqueness of the solutions are proved. The optimal error estimates for these schemes are obtained. Finally, a numerical example is provided to examine the efficiency of the proposed schemes.
基金the National Natural Science Foundation of China and China State Key Project for Basic Researches
文摘In this paper, we study the mixed element method for Sobolev equations. A time-discretization procedure is presented and analysed and the optimal order error estimates are derived.For convenience in practical computation, an alternating-direction iterative scheme of the mixed fi-nite element method is formulated and its stability and converbence are proved for the linear prob-lem. A numerical example is provided at the end of this paper.
基金Supported by the National Natural Science Fund(11061021)Supported by the Scientific Research Projection of Higher Schools of Inner Mongolia(NJZZ12011, NJ10006)+1 种基金Supported by the Program of Higher-level talents of Inner Mongolia University(125119)Supported by the Scientific Research Projection of Inner Mongolia University of Finance and Economics(KY1101)
文摘An H1-Galerkin expanded mixed finite element method is discussed for a class of second order semi-linear hyperbolic wave equations. By using the mixed formulation, we can get the optimal approximation for three variables: the scalar unknown, its gradient and its flux(coefficient times the gradient), simultaneously. We also prove the existence and uniqueness of semi-discrete solution. Finally, we obtain some numerical results to illustrate the efficiency of the method.
基金partially supported by National Natural Science Foundation of China (10531020)the National Basic Research Program of China (2006CB805902)+1 种基金the Project STCSM(06JC14005)the Doctorial Foundation of National Educational Ministry (20050246001)
文摘This paper is devoted to the Tricomi problem for a mixed type equation of second order. The coeffcients are assumed to be discontinuous on the line where the type is changed. The unique existence of the solution to the problem is proved if the domain is small enough. Correspondingly, some estimates on the solution is also established.
文摘The present article deals with oblique derivative problems for some nonlinear mixed equations with parabolic degeneracy, which include the Tricomi problem as a special case. First, the formulation of the problems for the equations is given; next, the representation and estimates of solutions for the above problems are obtained; finally, the existence of solutions for the problems is proved by the successive iteration and the compactness principle of solutions of the problems. In this article, the author uses the complex method, namely, the complex functions in the elliptic domain and the hyperbolic complex functions in hyperbolic domain are used.
基金Supported by by the National Science Foundation for Young Scholars of China(11101431)the Fundamental Research Funds for the Central Universities (12CX04082A,10CX04041A)Shandong Province Natural Science Foundation of China(ZR2010AL020)
文摘Two new convection-dominated are derived under the approximate solutions least-squares mixed finite element procedures are formulated for solving Sobolev equations. Optimal H(div;Ω)×H1(Ω) norms error estimates standard mixed finite spaces. Moreover, these two schemes provide the with first-order and second-order accuracy in time increment, respectively.
文摘The objective of this paper is to study the oscillatory and asymptotic properties of the mixed type third order neutral difference equation of the form△(an△^2(xn+bnxn-τ1+cnxn+τ2))+qnx^βn+1-σ1+pnx^^βn+1+σ2=0,where (an), (bn}, (cn}, (qn} and (pn} are positive real sequences, β is a ratio of odd positive integers, τ1, τ2, and σ2 are positive integers. We establish some sufficient conditions which ensure that all solutions are either oscillatory or converges to zero. Some examples are presented to illustrate the main results.
基金supported by the National Natural Science Foundation of China (No. 10601022)NSF ofInner Mongolia Autonomous Region of China (No. 200607010106)513 and Science Fund of InnerMongolia University for Distinguished Young Scholars (No. ND0702)
文摘A mixed time discontinuous space-time finite element scheme for secondorder convection diffusion problems is constructed and analyzed. Order of the equation is lowered by the mixed finite element method. The low order equation is discretized with a space-time finite element method, continuous in space but discontinuous in time. Stability, existence, uniqueness and convergence of the approximate solutions are proved. Numerical results are presented to illustrate efficiency of the proposed method.
基金Supported by National Natural Science Foundation of China (11071198 11101347)+2 种基金Postdoctor Foundation of China (2012M510363)the Key Project in Science and Technology Research Plan of the Education Department of Hubei Province (D20112605 D20122501)
文摘The existence and multiplicity of positive solutions are studied for a class of quasi- linear elliptic equations involving Sobolev critical exponents with mixed Dirichlet-Neumann boundary conditions by the variational methods and some analytical techniques.
基金Supported by National Natural Science Fund of China (11061021)Key Project of Chinese Ministry of Education (12024)+2 种基金Natural Science Fund of Inner Mongolia Autonomous Region (2012MS0108,2012MS0106,2011BS0102)Scientific Research Projection of Higher Schools of Inner Mongolia (NJZZ12011,NJZY13199)Program of Higher-level talents of Inner Mongolia University (125119,Z200901004,30105-125132)
文摘A new mixed scheme which combines the variation of constants and the H1-Galerkin mixed finite element method is constructed for nonlinear Sobolev equation with nonlinear con- vection term. Optimal error estimates are derived for both semidiscrete and fully discrete schemes. Finally, some numerical results are given to confirm the theoretical analysis of the proposed method.
文摘Through the paper, a general solution of a mixed type functional equation in fuzzy Banach space is obtained and by using the fixed point method a generalized Hyers-Ulam-Rassias stability of the mixed type functional equation in fuzzy Banach space is proved.
文摘In this paper, we obtained some sufficient conditions for the oscillation of all solutions of the second order neutral differential equation of the form where , and . Examples are provided to illustrate the main results.
基金supported by the National Key R&D Program of China(2020YFA0712900)the National Natural Science Foundation of China(11531001).
文摘A continuous time and mixed state branching process is constructed by a scaling limit theorem of two-type Galton-Watson processes.The process can also be obtained by the pathwise unique solution to a stochastic equation system.From the stochastic equation system we derive the distribution of local jumps and give the exponential ergodicity in Wasserstein-type distances of the transition semigroup.Meanwhile,we study immigration structures associated with the process and prove the existence of the stationary distribution of the process with immigration.