A multiscale mortar multipoint flux mixed finite element method

Wheeler, Mary Fanett; Xue, Guangri; Yotov, Ivan

A multiscale mortar multipoint flux mixed finite element method

Type

Article

Authors

Wheeler, Mary Fanett
Xue, Guangri
Yotov, Ivan

KAUST Grant Number

KUS-F1-032-04

Online Publication Date

2012-02-03

Print Publication Date

2012-07

Date

2012-02-03

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. © EDP Sciences, SMAI, 2012.

Citation

Wheeler MF, Xue G, Yotov I (2012) A multiscale mortar multipoint flux mixed finite element method. ESAIM: Mathematical Modelling and Numerical Analysis 46: 759–796. Available: http://dx.doi.org/10.1051/m2an/2011064.

Acknowledgements

partially supported by the NSF-CDI under contract number DMS 0835745, the DOE grant DE-FGO2-04ER25617, and the Center for Frontiers of Subsurface Energy Security under Contract No. DE-SC0001114.supported by Award No. KUS-F1-032-04, made by King Abdullah University of Science and Technology (KAUST).partially supported by the DOE grant DE-FG02-04ER25618, the NSF grant DMS 0813901, and the J. Tinsley Oden Faculty Fellowship, ICES, The University of Texas at Austin.