A two-grid partition of unity method for second order elliptic problems is proposed and analyzed. The standard two-grid method is a local and parallel method usually leading to a discontinuous solution in the entire c...A two-grid partition of unity method for second order elliptic problems is proposed and analyzed. The standard two-grid method is a local and parallel method usually leading to a discontinuous solution in the entire computational domain. Partition of unity method is employed to glue all the local solutions together to get the global continuous one, which is optimal in HI-norm. Furthermore, it is shown that the L^2 error can be improved by using the coarse grid correction. Numerical experiments are reported to support the theoretical results.展开更多
In this paper, the method of non-conforming mixed finite element for second order elliptic problems is discussed and a format of real optimal order for the lowest order error estimate.
This paper is devoted to study of an iterative procedure for domain decomposition method of second order elliptic problem with mixed boundary conditions (i.e., Dirichlet condition on a part of boundary and Neumann con...This paper is devoted to study of an iterative procedure for domain decomposition method of second order elliptic problem with mixed boundary conditions (i.e., Dirichlet condition on a part of boundary and Neumann condition on the another part of boundary). For the pure Dirichlet problem, Marini and Quarteroni [3], [4] considered a similar approach, which is extended to more complex problem in this paper.展开更多
In this paper,a new hybridized mixed formulation of weak Galerkin method is studied for a second order elliptic problem.This method is designed by approximate some operators with discontinuous piecewise polynomials in...In this paper,a new hybridized mixed formulation of weak Galerkin method is studied for a second order elliptic problem.This method is designed by approximate some operators with discontinuous piecewise polynomials in a shape regular finite element partition.Some discrete inequalities are presented on discontinuous spaces and optimal order error estimations are established.Some numerical results are reported to show super convergence and confirm the theory of the mixed weak Galerkin method.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
基金Project supported by the National Natural Science Foundation of China(No.40074031)the Science Foundation of the Science and Technology Commission of Shanghai Municipalitythe Program for Young Excellent Talents in Tongji University(No.2007kj008)
文摘A two-grid partition of unity method for second order elliptic problems is proposed and analyzed. The standard two-grid method is a local and parallel method usually leading to a discontinuous solution in the entire computational domain. Partition of unity method is employed to glue all the local solutions together to get the global continuous one, which is optimal in HI-norm. Furthermore, it is shown that the L^2 error can be improved by using the coarse grid correction. Numerical experiments are reported to support the theoretical results.
基金Project supported by the Cultivating Foundation of Youthful Backbone of Science and Technologyof Beijing, the National Science
文摘In this paper, the method of non-conforming mixed finite element for second order elliptic problems is discussed and a format of real optimal order for the lowest order error estimate.
文摘This paper is devoted to study of an iterative procedure for domain decomposition method of second order elliptic problem with mixed boundary conditions (i.e., Dirichlet condition on a part of boundary and Neumann condition on the another part of boundary). For the pure Dirichlet problem, Marini and Quarteroni [3], [4] considered a similar approach, which is extended to more complex problem in this paper.
文摘In this paper,a new hybridized mixed formulation of weak Galerkin method is studied for a second order elliptic problem.This method is designed by approximate some operators with discontinuous piecewise polynomials in a shape regular finite element partition.Some discrete inequalities are presented on discontinuous spaces and optimal order error estimations are established.Some numerical results are reported to show super convergence and confirm the theory of the mixed weak Galerkin method.
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.
