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
H1-Galerkin mixed methods are proposed for viscoelasticity wave equation.Depending on the physical quantities of interest,two methods are discussed.The optimal error estimates and the proof of the existence and unique...H1-Galerkin mixed methods are proposed for viscoelasticity wave equation.Depending on the physical quantities of interest,two methods are discussed.The optimal error estimates and the proof of the existence and uniqueness of semidiscrete solutions are derived for problems in one space dimension.And the methods don＇t require the LBB condition.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
In this paper,we present a two-grid discretization scheme for semilinear parabolic integro-differential equations by H1-Galerkin mixed finite element methods.We use the lowest order Raviart-Thomas mixed finite element...In this paper,we present a two-grid discretization scheme for semilinear parabolic integro-differential equations by H1-Galerkin mixed finite element methods.We use the lowest order Raviart-Thomas mixed finite elements and continuous linear finite element for spatial discretization,and backward Euler scheme for temporal discretization.Firstly,a priori error estimates and some superclose properties are derived.Secondly,a two-grid scheme is presented and its convergence is discussed.In the proposed two-grid scheme,the solution of the nonlinear system on a fine grid is reduced to the solution of the nonlinear system on a much coarser grid and the solution of two symmetric and positive definite linear algebraic equations on the fine grid and the resulting solution still maintains optimal accuracy.Finally,a numerical experiment is implemented to verify theoretical results of the proposed scheme.The theoretical and numerical results show that the two-grid method achieves the same convergence property as the one-grid method with the choice h=H^(2).展开更多
A nonconforming H^1-Calerkin mixed finite element method is analyzed for Sobolev equations on anisotropic meshes. The error estimates are obtained without using Ritz-Volterra projection.
In classical mixed finite element method, the choice of the finite element approximating spaces is restricted by the imposition of the LBB consistency condition. The method of H1-Galerkin mixed finite element method a...In classical mixed finite element method, the choice of the finite element approximating spaces is restricted by the imposition of the LBB consistency condition. The method of H1-Galerkin mixed finite element method avoids completely the imposition of such a condition on the approximating spaces. In this article, we discuss and analyze error estimates for Convection-dominated diffusion problems using H1-Galerkin mixed finite element method, along with the method of characteristics. Optimal order of convergence has been achieved for the error estimates of a two-step Euler backward difference scheme.展开更多
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 NNSF(10601022,11061021)Supported by NSF of Inner Mongolia Au-tonomous Region(200607010106)Supported by SRP of Higher Schools of Inner Mongolia(NJ10006)
文摘H1-Galerkin mixed methods are proposed for viscoelasticity wave equation.Depending on the physical quantities of interest,two methods are discussed.The optimal error estimates and the proof of the existence and uniqueness of semidiscrete solutions are derived for problems in one space dimension.And the methods don＇t require the LBB condition.
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.
基金Science and Technology Research Project of Jilin Provincial Department of Education(JJKH20190634KJ)The work of C.M.Liu was supported by the National Natural Science Foundation of China(11901189)+5 种基金the Key Project of Hunan Provincial Education Department(19A191)L.P.Chen was supported by Natural Science Foundation of China(11501473)the Fundamental Research Funds of the Central Universities of China(2682016CX108)The work of Y.Yang was supported by National Natural Science Foundation of China Project(11671342,11771369,11931003)the Project of Scientific Research Fund of Hunan Provincial Science and Technology Department(2018JJ2374,2018WK4006,2019YZ3003)the Key Project of Hunan Provincial Department of Education(17A210).
文摘In this paper,we present a two-grid discretization scheme for semilinear parabolic integro-differential equations by H1-Galerkin mixed finite element methods.We use the lowest order Raviart-Thomas mixed finite elements and continuous linear finite element for spatial discretization,and backward Euler scheme for temporal discretization.Firstly,a priori error estimates and some superclose properties are derived.Secondly,a two-grid scheme is presented and its convergence is discussed.In the proposed two-grid scheme,the solution of the nonlinear system on a fine grid is reduced to the solution of the nonlinear system on a much coarser grid and the solution of two symmetric and positive definite linear algebraic equations on the fine grid and the resulting solution still maintains optimal accuracy.Finally,a numerical experiment is implemented to verify theoretical results of the proposed scheme.The theoretical and numerical results show that the two-grid method achieves the same convergence property as the one-grid method with the choice h=H^(2).
基金Supported by National Natural Science Funds of China(No.11361035)the National Science Foundation of Inner Mongolia Province(No.2012MS0106)+1 种基金Scientific Research Projection of Higher Schools of Inner Mongolia(No.NJZY14013)Program of Higher Level Talents of Inner Mongolia University(No.135127)~~
基金Supported by the National Natural Science Foundation of China(No.10671184).
文摘A nonconforming H^1-Calerkin mixed finite element method is analyzed for Sobolev equations on anisotropic meshes. The error estimates are obtained without using Ritz-Volterra projection.
文摘In classical mixed finite element method, the choice of the finite element approximating spaces is restricted by the imposition of the LBB consistency condition. The method of H1-Galerkin mixed finite element method avoids completely the imposition of such a condition on the approximating spaces. In this article, we discuss and analyze error estimates for Convection-dominated diffusion problems using H1-Galerkin mixed finite element method, along with the method of characteristics. Optimal order of convergence has been achieved for the error estimates of a two-step Euler backward difference scheme.
