Numerische Mathematik

, Volume 121, Issue 1, pp 165–204 | Cite as

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



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.

Mathematics Subject Classification (2000)

65N06 65N08 65N12 65N15 65N22 65N30 76S05 


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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Center for Subsurface Modeling, Institute for Computational Engineering and SciencesThe University of Texas at AustinAustinUSA
  2. 2.Department of MathematicsUniversity of PittsburghPittsburghUSA

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