A multipoint flux mixed finite element method on distorted quadrilaterals and hexahedra |
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Authors: | Mary Wheeler Guangri Xue Ivan Yotov |
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Institution: | 1. Center for Subsurface Modeling, Institute for Computational Engineering and Sciences, The University of Texas at Austin, 201 E 24th Street, Austin, TX, 78712, USA 2. Department of Mathematics, University of Pittsburgh, 301 Thackeray Hall, Pittsburgh, PA, 15260, USA
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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. |
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Keywords: | |
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