A multipoint flux mixed finite element method on distorted quadrilaterals and hexahedra
KAUST Grant NumberKUS-F1-032-04
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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.
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.
SponsorsMary 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.