Superconvergence and Postprocessing of Fluxes from Lowest-Order Mixed Methods on Triangles and Tetrahedra
Autor: | Philip T. Keenan, Todd F. Dupont |
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Rok vydání: | 1998 |
Předmět: | |
Zdroj: | SIAM Journal on Scientific Computing. 19:1322-1332 |
ISSN: | 1095-7197 1064-8275 |
DOI: | 10.1137/s1064827595280417 |
Popis: | 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. |
Databáze: | OpenAIRE |
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