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.
Mots-clés : multiscale, mixed finite element, mortar finite element, multipoint flux approximation, cell-centered finite difference, full tensor coefficient, multiblock, nonmatching grids, quadrilaterals, hexahedra
@article{M2AN_2012__46_4_759_0,
author = {Wheeler, Mary Fanett and Xue, Guangri and Yotov, Ivan},
title = {A multiscale mortar multipoint flux mixed finite element method},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {759--796},
publisher = {EDP-Sciences},
volume = {46},
number = {4},
year = {2012},
doi = {10.1051/m2an/2011064},
mrnumber = {2891469},
zbl = {1275.65082},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2011064/}
}
TY - JOUR AU - Wheeler, Mary Fanett AU - Xue, Guangri AU - Yotov, Ivan TI - A multiscale mortar multipoint flux mixed finite element method JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2012 SP - 759 EP - 796 VL - 46 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2011064/ DO - 10.1051/m2an/2011064 LA - en ID - M2AN_2012__46_4_759_0 ER -
%0 Journal Article %A Wheeler, Mary Fanett %A Xue, Guangri %A Yotov, Ivan %T A multiscale mortar multipoint flux mixed finite element method %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2012 %P 759-796 %V 46 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2011064/ %R 10.1051/m2an/2011064 %G en %F M2AN_2012__46_4_759_0
Wheeler, Mary Fanett; Xue, Guangri; Yotov, Ivan. A multiscale mortar multipoint flux mixed finite element method. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 46 (2012) no. 4, pp. 759-796. doi : 10.1051/m2an/2011064. http://www.numdam.org/articles/10.1051/m2an/2011064/
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