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

  • Authors:

  • Mary Wheeler;Guangri Xue;Ivan Yotov

  • Affiliations:

  • The University of Texas at Austin, Center for Subsurface Modeling, Institute for Computational Engineering and Sciences, 201 E 24th Street, 78712, Austin, TX, USA;The University of Texas at Austin, Center for Subsurface Modeling, Institute for Computational Engineering and Sciences, 201 E 24th Street, 78712, Austin, TX, USA;University of Pittsburgh, Department of Mathematics, 301 Thackeray Hall, 15260, Pittsburgh, PA, USA

  • Venue:
  • Numerische Mathematik
  • Year:
  • 2012

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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.