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A multiscale mortar multipoint flux mixed finite element method

Published online by Cambridge University Press:  03 February 2012

Mary Fanett Wheeler ,
Guangri Xue  and
Ivan Yotov
Mary Fanett Wheeler
Affiliation:
Center for Subsurface Modeling, Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, 78712 TX, USA. mfw@ices.utexas.edu
Guangri Xue
Affiliation:
Center for Subsurface Modeling, Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, 78712 TX, USA; gxue@ices.utexas.edu
Ivan Yotov
Affiliation:
Department of Mathematics, University of Pittsburgh, Pittsburgh, 15260 PA, USA; yotov@math.pitt.edu
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Abstract

In this paper, we develop a multiscale mortar multipoint flux mixed finite element method for second order elliptic problems. The equations in the coarse elements (or subdomains) are discretized on a fine grid scale by a multipoint flux mixed finite element method that reduces to cell-centered finite differences on irregular grids. The subdomain grids do not have to match across the interfaces. Continuity of flux between coarse elements is imposed via a mortar finite element space on a coarse grid scale. With an appropriate choice of polynomial degree of the mortar space, we derive optimal order convergence on the fine scale for both the multiscale pressure and velocity, as well as the coarse scale mortar pressure. Some superconvergence results are also derived. The algebraic system is reduced via a non-overlapping domain decomposition to a coarse scale mortar interface problem that is solved using a multiscale flux basis. Numerical experiments are presented to confirm the theory and illustrate the efficiency and flexibility of the method.

Keywords

Multiscalemixed finite elementmortar finite elementmultipoint flux approximationcell-centered finite differencefull tensor coefficientmultiblocknonmatching gridsquadrilateralshexahedra
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 46 , Issue 4 , July 2012 , pp. 759 - 796
Copyright
© EDP Sciences, SMAI, 2012

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References

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