The convergence analysis of the lower order nonconforming element pro- posed by Park and Sheen is applied to the second-order elliptic problem under anisotropic meshes. The corresponding error estimation is obtained. ...The convergence analysis of the lower order nonconforming element pro- posed by Park and Sheen is applied to the second-order elliptic problem under anisotropic meshes. The corresponding error estimation is obtained. Moreover, by using the interpo- lation postprocessing technique, a global superconvergence property for the discretization error of the postprocessed discrete solution to the solution itself is derived. Numerical results are also given to verify the theoretical analysis.展开更多
In this paper, a new higher order Wilson element is presented, and the convergence is proved. Then the interpolation postprocessing technique is used to obtain the global superconvergence and posterior error estimate ...In this paper, a new higher order Wilson element is presented, and the convergence is proved. Then the interpolation postprocessing technique is used to obtain the global superconvergence and posterior error estimate of higher accuracy of this new element for the Sobolev type equations.展开更多
The post-processing procedure is given by a interpolant postprocessing of the finit element solution by appropriately-define finite dimensional subspaces, The corresponding superconvergence are established on general ...The post-processing procedure is given by a interpolant postprocessing of the finit element solution by appropriately-define finite dimensional subspaces, The corresponding superconvergence are established on general quasi-regular finite element partitions.展开更多
Abstract. In this paper which is motivated by computation on parallel machine, we showthat the superconvergence results of the finite element method(FEM) with Lagrange mul-tipliers based on domain decomposition method...Abstract. In this paper which is motivated by computation on parallel machine, we showthat the superconvergence results of the finite element method(FEM) with Lagrange mul-tipliers based on domain decomposition method (DDM) with nonmatching grids can becarried over to parabolic problems. The main idea of this paper is to achieve the combina-tion of parallel computational method with the higher accuracy technique by interpolationfinite element postprocessing.展开更多
Provides information on a study which discussed the convergence and superconvergence for eigenvalue problem of the biharmonic equation using the Hermite bicubic element. Discussion on eigenvalue problem for biharmonic...Provides information on a study which discussed the convergence and superconvergence for eigenvalue problem of the biharmonic equation using the Hermite bicubic element. Discussion on eigenvalue problem for biharmonic equation; Background on asymptotic error expansions and interpolation postprocessing; Superconvergence approximations to the eigenvalue and eigenfunction.展开更多
In this paper, the Wilson nonconforming finite element is considered for solving elliptic eigenvalue problems. Based on an interpolation postprocessing, superconvergence estimates of both eigenfunction and eigenvalue...In this paper, the Wilson nonconforming finite element is considered for solving elliptic eigenvalue problems. Based on an interpolation postprocessing, superconvergence estimates of both eigenfunction and eigenvalue are obtained.展开更多
In this paper,we consider the energy conserving numerical scheme for coupled nonlinear Klein-Gordon equations.We propose energy conserving finite element method and get the unconditional superconvergence resultO(h^(2)...In this paper,we consider the energy conserving numerical scheme for coupled nonlinear Klein-Gordon equations.We propose energy conserving finite element method and get the unconditional superconvergence resultO(h^(2)+Dt^(2))by using the error splitting technique and postprocessing interpolation.Numerical experiments are carried out to support our theoretical results.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.10371113,10471133 and 10590353)
文摘The convergence analysis of the lower order nonconforming element pro- posed by Park and Sheen is applied to the second-order elliptic problem under anisotropic meshes. The corresponding error estimation is obtained. Moreover, by using the interpo- lation postprocessing technique, a global superconvergence property for the discretization error of the postprocessed discrete solution to the solution itself is derived. Numerical results are also given to verify the theoretical analysis.
基金the National Natural Science Foundation of China(10671184)
文摘In this paper, a new higher order Wilson element is presented, and the convergence is proved. Then the interpolation postprocessing technique is used to obtain the global superconvergence and posterior error estimate of higher accuracy of this new element for the Sobolev type equations.
基金the Foundation of Natonal Natural Science of China and the Foundation of Aducation of Hunan Province.
文摘The post-processing procedure is given by a interpolant postprocessing of the finit element solution by appropriately-define finite dimensional subspaces, The corresponding superconvergence are established on general quasi-regular finite element partitions.
文摘Abstract. In this paper which is motivated by computation on parallel machine, we showthat the superconvergence results of the finite element method(FEM) with Lagrange mul-tipliers based on domain decomposition method (DDM) with nonmatching grids can becarried over to parabolic problems. The main idea of this paper is to achieve the combina-tion of parallel computational method with the higher accuracy technique by interpolationfinite element postprocessing.
文摘Provides information on a study which discussed the convergence and superconvergence for eigenvalue problem of the biharmonic equation using the Hermite bicubic element. Discussion on eigenvalue problem for biharmonic equation; Background on asymptotic error expansions and interpolation postprocessing; Superconvergence approximations to the eigenvalue and eigenfunction.
文摘In this paper, the Wilson nonconforming finite element is considered for solving elliptic eigenvalue problems. Based on an interpolation postprocessing, superconvergence estimates of both eigenfunction and eigenvalue are obtained.
基金The work is supported by the National Natural Science Foundation of China(No.11871441)Beijing Natural Science Foundation(No.1192003).
文摘In this paper,we consider the energy conserving numerical scheme for coupled nonlinear Klein-Gordon equations.We propose energy conserving finite element method and get the unconditional superconvergence resultO(h^(2)+Dt^(2))by using the error splitting technique and postprocessing interpolation.Numerical experiments are carried out to support our theoretical results.
