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

Mary Wheeler, Guangri Xue, Ivan Yotov

Research output: Contribution to journalArticlepeer-review

70 Scopus citations


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
Issue number1
StatePublished - Nov 6 2011
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-F1-032-04
Acknowledgements: Mary Wheeler is supported by the NSF-CDI under contract number DMS 0835745,the DOE grant DE-FG02-04ER25617, and the Center for Frontiers of Subsurface Energy Security underContract No. DE-SC0001114. Guangri Xue is supported by Award No. KUS-F1-032-04, made by KingAbdullah University of Science and Technology (KAUST). Ivan Yotov is partially supported by the DOEgrant DE-FG02-04ER25618, the NSF grant DMS 0813901, and the J. Tinsley Oden Faculty Fellowship,ICES, The University of Texas at Austin.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.


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