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

Handle URI:
http://hdl.handle.net/10754/597262
Title:
A Family of Multipoint Flux Mixed Finite Element Methods for Elliptic Problems on General Grids
Authors:
Wheeler, Mary F.; Xue, Guangri; Yotov, Ivan
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.
Citation:
Wheeler 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.
Publisher:
Elsevier BV
Journal:
Procedia Computer Science
KAUST Grant Number:
KUS-F1-032-04
Conference/Event name:
11th International Conference on Computational Science, ICCS 2011
Issue Date:
2011
DOI:
10.1016/j.procs.2011.04.097
Type:
Conference Paper
ISSN:
1877-0509
Sponsors:
1 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.
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Full metadata record

DC FieldValue Language
dc.contributor.authorWheeler, Mary F.en
dc.contributor.authorXue, Guangrien
dc.contributor.authorYotov, Ivanen
dc.date.accessioned2016-02-25T12:29:17Zen
dc.date.available2016-02-25T12:29:17Zen
dc.date.issued2011en
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.en
dc.identifier.issn1877-0509en
dc.identifier.doi10.1016/j.procs.2011.04.097en
dc.identifier.urihttp://hdl.handle.net/10754/597262en
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.en
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.en
dc.publisherElsevier BVen
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/en
dc.subjectCell-centered finite differenceen
dc.subjectFull tensoren
dc.subjectHexahedraen
dc.subjectMixed finite elementen
dc.subjectMultipoint flux approximationen
dc.subjectQuadrilateralsen
dc.subjectSimplicesen
dc.subjectTriangular prismsen
dc.titleA Family of Multipoint Flux Mixed Finite Element Methods for Elliptic Problems on General Gridsen
dc.typeConference Paperen
dc.identifier.journalProcedia Computer Scienceen
dc.conference.date2011-06-01 to 2011-06-03en
dc.conference.name11th International Conference on Computational Science, ICCS 2011en
dc.conference.locationSingapore, SGPen
dc.contributor.institutionUniversity of Texas at Austin, Austin, United Statesen
dc.contributor.institutionUniversity of Pittsburgh, Pittsburgh, United Statesen
kaust.grant.numberKUS-F1-032-04en
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