Abstract
Certain finite difference methods on rectangular grids for second-order elliptic equations are known to yield superconvergent flux approximations. A class of related finite difference methods recently have been defined for triangular meshes by applying special quadrature rules to an extended version of a mixed finite element method by Arbogast, Dawson, and Keenan [Mixed Finite Element Methods as Finite Difference Methods for Solving Elliptic Equations on Triangular Elements, Tech. report 93-53, Dept. of Computational and Applied Mathematics, Rice University, Houston, TX, 1993; in Computational Methods in Water Resources, Kluwer Academic Publishers, Norwell, MA, 1994]; the usual hybrid mixed method can also be applied to meshes of triangular and tetrahedral elements. Unfortunately, the flux vectors from these methods are only first-order accurate. Empirical evidence indicates that a local postprocessing technique described by Keenan in [An Efficient Postprocessor for Velocities from Mixed Methods on Triangular Elements, Dept. of Computational and Applied Mathematics, Tech. report 94-22, Rice University, Houston, TX, 1994] recovers second-order accurate velocities at special points. In this paper, a class of local postprocessing techniques generalizing the one in [An Efficient Postprocessor for Velocities from Mixed Methods on Triangular Elements, Tech. report 94-22, Rice University, Houston, TX, 1994] are presented and analyzed. These postprocessors are shown to recover second-order accurate velocity fields on three lines meshes. Numerical experiments illustrate these results and investigate more general situations, including meshes of tetrahedral elements.
Published Version
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