A Family of Multipoint Flux Mixed Finite Element Methods for Elliptic Problems on General Grids | Zendy

Mary F. Wheeler | Zendy; Guangri Xue | Zendy; Ivan Yotov | Zendy

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A Family of Multipoint Flux Mixed Finite Element Methods for Elliptic Problems on General Grids

Author(s) -

Mary F. Wheeler,

Guangri Xue,

Ivan Yotov

Publication year - 2011

Publication title -

procedia computer science

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.334

H-Index - 76

ISSN - 1877-0509

DOI - 10.1016/j.procs.2011.04.097

Subject(s) - quadrilateral , superconvergence , finite element method , gaussian quadrature , quadrature (astronomy) , mixed finite element method , hexahedron , discontinuous galerkin method , extended finite element method , mathematics , computer science , mathematical analysis , nyström method , physics , integral equation , optics , thermodynamics

In this paper, we discuss a family of multipoint flux mixed finite element (MFMFE) methods on simplicial, quadrilateral, hexahedral, and triangular-prismatic grids. The MFMFE methods are locally conservative with continuous normal fluxes, since they are developed within a variational framework as mixed finite element methods with special approximating spaces and quadrature rules. The latter allows for local flux elimination giving a cell-centered system for the scalar variable. We study two versions of the method: with a symmetric quadrature rule on smooth grids and a non-symmetric quadrature rule on rough grids. Theoretical and numerical results demonstrate first order convergence for problems with full-tensor coeffcients. Second order superconvergence is observed on smooth grids

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