# A multiscale mortar multipoint flux mixed finite element method

Mary Fanett Wheeler; Guangri Xue; Ivan Yotov

ESAIM: Mathematical Modelling and Numerical Analysis (2012)

- Volume: 46, Issue: 4, page 759-796
- ISSN: 0764-583X

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topWheeler, Mary Fanett, Xue, Guangri, and Yotov, Ivan. "A multiscale mortar multipoint flux mixed finite element method." ESAIM: Mathematical Modelling and Numerical Analysis 46.4 (2012): 759-796. <http://eudml.org/doc/277847>.

@article{Wheeler2012,

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.},

author = {Wheeler, Mary Fanett, Xue, Guangri, Yotov, Ivan},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Multiscale; mixed finite element; mortar finite element; multipoint flux approximation; cell-centered finite difference; full tensor coefficient; multiblock; nonmatching grids; quadrilaterals; hexahedra; mixed finite element method; second-order elliptic problems; convergence; superconvergence; domain decomposition; numerical experiments},

language = {eng},

month = {2},

number = {4},

pages = {759-796},

publisher = {EDP Sciences},

title = {A multiscale mortar multipoint flux mixed finite element method},

url = {http://eudml.org/doc/277847},

volume = {46},

year = {2012},

}

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

DA - 2012/2//

PB - EDP Sciences

VL - 46

IS - 4

SP - 759

EP - 796

AB - 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.

LA - eng

KW - Multiscale; mixed finite element; mortar finite element; multipoint flux approximation; cell-centered finite difference; full tensor coefficient; multiblock; nonmatching grids; quadrilaterals; hexahedra; mixed finite element method; second-order elliptic problems; convergence; superconvergence; domain decomposition; numerical experiments

UR - http://eudml.org/doc/277847

ER -

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