A Family of Multipoint Flux Mixed Finite Element Methods for Elliptic Problems on General Grids
dc.contributor.author | Wheeler, Mary F. | |
dc.contributor.author | Xue, Guangri | |
dc.contributor.author | Yotov, Ivan | |
dc.date.accessioned | 2016-02-25T12:29:17Z | |
dc.date.available | 2016-02-25T12:29:17Z | |
dc.date.issued | 2011 | |
dc.identifier.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. | |
dc.identifier.issn | 1877-0509 | |
dc.identifier.doi | 10.1016/j.procs.2011.04.097 | |
dc.identifier.uri | http://hdl.handle.net/10754/597262 | |
dc.description.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. | |
dc.description.sponsorship | 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. | |
dc.publisher | Elsevier BV | |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/ | |
dc.subject | Cell-centered finite difference | |
dc.subject | Full tensor | |
dc.subject | Hexahedra | |
dc.subject | Mixed finite element | |
dc.subject | Multipoint flux approximation | |
dc.subject | Quadrilaterals | |
dc.subject | Simplices | |
dc.subject | Triangular prisms | |
dc.title | A Family of Multipoint Flux Mixed Finite Element Methods for Elliptic Problems on General Grids | |
dc.type | Conference Paper | |
dc.identifier.journal | Procedia Computer Science | |
dc.conference.date | 2011-06-01 to 2011-06-03 | |
dc.conference.name | 11th International Conference on Computational Science, ICCS 2011 | |
dc.conference.location | Singapore, SGP | |
dc.contributor.institution | University of Texas at Austin, Austin, United States | |
dc.contributor.institution | University of Pittsburgh, Pittsburgh, United States | |
kaust.grant.number | KUS-F1-032-04 |