A multiscale mortar multipoint flux mixed finite element method

Handle URI:
http://hdl.handle.net/10754/597327
Title:
A multiscale mortar multipoint flux mixed finite element method
Authors:
Wheeler, Mary Fanett; Xue, Guangri; Yotov, Ivan
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.
Publisher:
EDP Sciences
Journal:
ESAIM: Mathematical Modelling and Numerical Analysis
KAUST Grant Number:
KUS-F1-032-04
Issue Date:
3-Feb-2012
DOI:
10.1051/m2an/2011064
Type:
Article
ISSN:
0764-583X; 1290-3841
Sponsors:
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.
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Full metadata record

DC FieldValue Language
dc.contributor.authorWheeler, Mary Fanetten
dc.contributor.authorXue, Guangrien
dc.contributor.authorYotov, Ivanen
dc.date.accessioned2016-02-25T12:30:46Zen
dc.date.available2016-02-25T12:30:46Zen
dc.date.issued2012-02-03en
dc.identifier.citationWheeler 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.en
dc.identifier.issn0764-583Xen
dc.identifier.issn1290-3841en
dc.identifier.doi10.1051/m2an/2011064en
dc.identifier.urihttp://hdl.handle.net/10754/597327en
dc.description.abstractIn 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.en
dc.description.sponsorshippartially 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.en
dc.publisherEDP Sciencesen
dc.subjectCell-centered finite differenceen
dc.subjectFull tensor coefficienten
dc.subjectHexahedraen
dc.subjectMixed finite elementen
dc.subjectMortar finite elementen
dc.subjectMultiblocken
dc.subjectMultipoint flux approximationen
dc.subjectMultiscaleen
dc.subjectNonmatching gridsen
dc.subjectQuadrilateralsen
dc.titleA multiscale mortar multipoint flux mixed finite element methoden
dc.typeArticleen
dc.identifier.journalESAIM: Mathematical Modelling and Numerical Analysisen
dc.contributor.institutionUniversity of Texas at Austin, Austin, United Statesen
dc.contributor.institutionUniversity of Pittsburgh, Pittsburgh, United Statesen
kaust.grant.numberKUS-F1-032-04en
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