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

Mary F. Wheeler, Guangri Xue, Ivan Yotov

Research output: Chapter in Book/Report/Conference proceedingConference contribution

13 Scopus citations

Abstract

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 coefficients. Second order superconvergence is observed on smooth grids. © 2011 Published by Elsevier Ltd.
Original languageEnglish (US)
Title of host publicationProcedia Computer Science
PublisherElsevier BV
Pages918-927
Number of pages10
DOIs
StatePublished - 2011
Externally publishedYes

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