In this paper we are concerned with a domain decomposition method with nonmatching grids for Raviart-Thomas finite elements. In this method, the normal complement of the resulting approximation is not continuous acros...In this paper we are concerned with a domain decomposition method with nonmatching grids for Raviart-Thomas finite elements. In this method, the normal complement of the resulting approximation is not continuous across the interface. To handle such non-conformity, a new matching condition will be introduced. Such matching condition still results in a symmetric and positive definite stiffness matrix. It will be shown that the approximate solution generated by the domain decomposition possesses the optimal energy error estimate.展开更多
This paper deals with Raviart-Thomas element (Q(2,1) x Q(1,2) - Q(1) element). Apart from its global superconvergence property of fourth order, we prove that a postprocessed extrapolation can globally increased the ac...This paper deals with Raviart-Thomas element (Q(2,1) x Q(1,2) - Q(1) element). Apart from its global superconvergence property of fourth order, we prove that a postprocessed extrapolation can globally increased the accuracy by fifth order.展开更多
In this paper,a residual type of a posteriori error estimator for the general second order elliptic eigenpair approximation by the mixed finite element method is derived and analyzed,based on a type of superconvergenc...In this paper,a residual type of a posteriori error estimator for the general second order elliptic eigenpair approximation by the mixed finite element method is derived and analyzed,based on a type of superconvergence result of the eigenfunction approximation.Its efficiency and reliability are proved by both theoretical analysis and numerical experiments.展开更多
We consider a nonlinear parabolic system describing compressible miscible displacement in a porous medium[4]. Continuous time and discrete time Galerkin methods are introduced to approximate the solution, and optimal ...We consider a nonlinear parabolic system describing compressible miscible displacement in a porous medium[4]. Continuous time and discrete time Galerkin methods are introduced to approximate the solution, and optimal H1-error estimates are obtained. This paper improves upon previously derived estimates in two aspects. Firstly, error estimates are given with no restrictions on the diffusion tensor. That is, we have included the effects of molecular diffusion and dispersion. Secondly, the complete compressible case is considered in the error analysis.展开更多
The aim of this paper is to provide a local superconvergence analysis for ined finite element methods of Poission equation. We shall prove that if p is smmoth enough in a local regionΩ0Ω1Ω and rectangular mesh is ...The aim of this paper is to provide a local superconvergence analysis for ined finite element methods of Poission equation. We shall prove that if p is smmoth enough in a local regionΩ0Ω1Ω and rectangular mesh is imposed onΩ1, then local superconvergence for are expected. Thus, by post-processing operators P and we have obtained the follwing local superconvergence error estimate:展开更多
基金supported by Special Funds for Major State Basic Research Projects of China(Grant No.1999032804)National Natural Science Foundation of China(Grant No.10371129).
文摘In this paper we are concerned with a domain decomposition method with nonmatching grids for Raviart-Thomas finite elements. In this method, the normal complement of the resulting approximation is not continuous across the interface. To handle such non-conformity, a new matching condition will be introduced. Such matching condition still results in a symmetric and positive definite stiffness matrix. It will be shown that the approximate solution generated by the domain decomposition possesses the optimal energy error estimate.
文摘This paper deals with Raviart-Thomas element (Q(2,1) x Q(1,2) - Q(1) element). Apart from its global superconvergence property of fourth order, we prove that a postprocessed extrapolation can globally increased the accuracy by fifth order.
基金supported by National Natural Science Foundation of China(Grant Nos.11001259,11031006,11071265,11201501 and 91230110)National Basic Research Program of China(973 Project)(Grant No. 2011CB309703)+3 种基金International S&T Cooperation Program of China(Grant No. 2010DFR00700)Croucher Foundation of Hong Kong Baptist Universitythe National Center for Mathematics and Interdisciplinary Science,CAS,the President Foundation of AMSS-CASthe Fundamental Research Funds for the CentralUniversities(Grant No. 2012121003)
文摘In this paper,a residual type of a posteriori error estimator for the general second order elliptic eigenpair approximation by the mixed finite element method is derived and analyzed,based on a type of superconvergence result of the eigenfunction approximation.Its efficiency and reliability are proved by both theoretical analysis and numerical experiments.
文摘We consider a nonlinear parabolic system describing compressible miscible displacement in a porous medium[4]. Continuous time and discrete time Galerkin methods are introduced to approximate the solution, and optimal H1-error estimates are obtained. This paper improves upon previously derived estimates in two aspects. Firstly, error estimates are given with no restrictions on the diffusion tensor. That is, we have included the effects of molecular diffusion and dispersion. Secondly, the complete compressible case is considered in the error analysis.
文摘The aim of this paper is to provide a local superconvergence analysis for ined finite element methods of Poission equation. We shall prove that if p is smmoth enough in a local regionΩ0Ω1Ω and rectangular mesh is imposed onΩ1, then local superconvergence for are expected. Thus, by post-processing operators P and we have obtained the follwing local superconvergence error estimate:
