A multipoint flux mixed finite element method on distorted quadrilaterals and hexahedra

Mary Wheeler, Guangri Xue, Ivan Yotov

Research output: Contribution to journalArticlepeer-review

57 Scopus citations

Abstract

In this paper, we develop a new mixed finite element method for elliptic problems on general quadrilateral and hexahedral grids that reduces to a cell-centered finite difference scheme. A special non-symmetric quadrature rule is employed that yields a positive definite cell-centered system for the pressure by eliminating local velocities. The method is shown to be accurate on highly distorted rough quadrilateral and hexahedral grids, including hexahedra with non-planar faces. Theoretical and numerical results indicate first-order convergence for the pressure and face fluxes. © 2011 Springer-Verlag.
Original languageEnglish (US)
Pages (from-to)165-204
Number of pages40
JournalNumerische Mathematik
Volume121
Issue number1
DOIs
StatePublished - Nov 6 2011
Externally publishedYes

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