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

Handle URI:
http://hdl.handle.net/10754/597324
Title:
A multipoint flux mixed finite element method on distorted quadrilaterals and hexahedra
Authors:
Wheeler, Mary; Xue, Guangri; Yotov, Ivan
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.
Citation:
Wheeler M, Xue G, Yotov I (2011) A multipoint flux mixed finite element method on distorted quadrilaterals and hexahedra. Numerische Mathematik 121: 165–204. Available: http://dx.doi.org/10.1007/s00211-011-0427-7.
Publisher:
Springer Nature
Journal:
Numerische Mathematik
KAUST Grant Number:
KUS-F1-032-04
Issue Date:
6-Nov-2011
DOI:
10.1007/s00211-011-0427-7
Type:
Article
ISSN:
0029-599X; 0945-3245
Sponsors:
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.
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Full metadata record

DC FieldValue Language
dc.contributor.authorWheeler, Maryen
dc.contributor.authorXue, Guangrien
dc.contributor.authorYotov, Ivanen
dc.date.accessioned2016-02-25T12:30:42Zen
dc.date.available2016-02-25T12:30:42Zen
dc.date.issued2011-11-06en
dc.identifier.citationWheeler M, Xue G, Yotov I (2011) A multipoint flux mixed finite element method on distorted quadrilaterals and hexahedra. Numerische Mathematik 121: 165–204. Available: http://dx.doi.org/10.1007/s00211-011-0427-7.en
dc.identifier.issn0029-599Xen
dc.identifier.issn0945-3245en
dc.identifier.doi10.1007/s00211-011-0427-7en
dc.identifier.urihttp://hdl.handle.net/10754/597324en
dc.description.abstractIn 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.en
dc.description.sponsorshipMary 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.en
dc.publisherSpringer Natureen
dc.titleA multipoint flux mixed finite element method on distorted quadrilaterals and hexahedraen
dc.typeArticleen
dc.identifier.journalNumerische Mathematiken
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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