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

dc.contributor.authorWheeler, Mary F.
dc.contributor.authorXue, Guangri
dc.contributor.authorYotov, Ivan
dc.date.accessioned2016-02-25T12:29:17Z
dc.date.available2016-02-25T12:29:17Z
dc.date.issued2011
dc.identifier.citationWheeler MF, Xue G, Yotov I (2011) A Family of Multipoint Flux Mixed Finite Element Methods for Elliptic Problems on General Grids. Procedia Computer Science 4: 918–927. Available: http://dx.doi.org/10.1016/j.procs.2011.04.097.
dc.identifier.issn1877-0509
dc.identifier.doi10.1016/j.procs.2011.04.097
dc.identifier.urihttp://hdl.handle.net/10754/597262
dc.description.abstractIn 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.
dc.description.sponsorship1 partially 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 under Contract No. DE-SC0001114.2 supported by Award No. KUS-F1-032-04, made by King Abdullah University of Science and Technology (KAUST).3 partially supported by the DOE grant DE-FG02-04ER25618, the NSF grant DMS 0813901, and the J. Tinsley Oden Faculty Fellowship, ICES, The University of Texas at Austin.
dc.publisherElsevier BV
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/
dc.subjectCell-centered finite difference
dc.subjectFull tensor
dc.subjectHexahedra
dc.subjectMixed finite element
dc.subjectMultipoint flux approximation
dc.subjectQuadrilaterals
dc.subjectSimplices
dc.subjectTriangular prisms
dc.titleA Family of Multipoint Flux Mixed Finite Element Methods for Elliptic Problems on General Grids
dc.typeConference Paper
dc.identifier.journalProcedia Computer Science
dc.conference.date2011-06-01 to 2011-06-03
dc.conference.name11th International Conference on Computational Science, ICCS 2011
dc.conference.locationSingapore, SGP
dc.contributor.institutionUniversity of Texas at Austin, Austin, United States
dc.contributor.institutionUniversity of Pittsburgh, Pittsburgh, United States
kaust.grant.numberKUS-F1-032-04


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