A Family of Multipoint Flux Mixed Finite Element Methods for Elliptic Problems on General Grids
KAUST Grant NumberKUS-F1-032-04
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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.
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.
Sponsors1 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.
JournalProcedia Computer Science
Conference/Event name11th International Conference on Computational Science, ICCS 2011
CollectionsPublications Acknowledging KAUST Support
Except where otherwise noted, this item's license is described as http://creativecommons.org/licenses/by-nc-nd/3.0/