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Article: Generalized multiscale finite element methods. nonlinear elliptic equations

TitleGeneralized multiscale finite element methods. nonlinear elliptic equations
Authors
KeywordsHigh-contrast
Generalized multiscale finite element method
Nonlinear equations
Issue Date2014
Citation
Communications in Computational Physics, 2014, v. 15, n. 3, p. 733-755 How to Cite?
AbstractIn this paper we use the Generalized Multiscale Finite Element Method (GMsFEM) framework, introduced in [26], in order to solve nonlinear elliptic equations with high-contrast coefficients. The proposed solution method involves linearizing the equation so that coarse-grid quantities of previous solution iterates can be regarded as auxiliary parameters within the problem formulation. With this convention, we systematically construct respective coarse solution spaces that lend themselves to either continuous Galerkin (CG) or discontinuous Galerkin (DG) global formulations. Here, we use Symmetric Interior Penalty Discontinuous Galerkin approach. Both methods yield a predictable error decline that depends on the respective coarse space dimension, and we illustrate the effectiveness of the CG and DG formulations by offering a variety of numerical examples. © 2014 Global-Science Press.
Persistent Identifierhttp://hdl.handle.net/10722/286889
ISSN
2020 Impact Factor: 3.246
2020 SCImago Journal Rankings: 1.217
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorEfendiev, Yalchin-
dc.contributor.authorGalvis, Juan-
dc.contributor.authorLi, Guanglian-
dc.contributor.authorPresho, Michael-
dc.date.accessioned2020-09-07T11:45:56Z-
dc.date.available2020-09-07T11:45:56Z-
dc.date.issued2014-
dc.identifier.citationCommunications in Computational Physics, 2014, v. 15, n. 3, p. 733-755-
dc.identifier.issn1815-2406-
dc.identifier.urihttp://hdl.handle.net/10722/286889-
dc.description.abstractIn this paper we use the Generalized Multiscale Finite Element Method (GMsFEM) framework, introduced in [26], in order to solve nonlinear elliptic equations with high-contrast coefficients. The proposed solution method involves linearizing the equation so that coarse-grid quantities of previous solution iterates can be regarded as auxiliary parameters within the problem formulation. With this convention, we systematically construct respective coarse solution spaces that lend themselves to either continuous Galerkin (CG) or discontinuous Galerkin (DG) global formulations. Here, we use Symmetric Interior Penalty Discontinuous Galerkin approach. Both methods yield a predictable error decline that depends on the respective coarse space dimension, and we illustrate the effectiveness of the CG and DG formulations by offering a variety of numerical examples. © 2014 Global-Science Press.-
dc.languageeng-
dc.relation.ispartofCommunications in Computational Physics-
dc.subjectHigh-contrast-
dc.subjectGeneralized multiscale finite element method-
dc.subjectNonlinear equations-
dc.titleGeneralized multiscale finite element methods. nonlinear elliptic equations-
dc.typeArticle-
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.4208/cicp.020313.041013a-
dc.identifier.scopuseid_2-s2.0-84892383543-
dc.identifier.volume15-
dc.identifier.issue3-
dc.identifier.spage733-
dc.identifier.epage755-
dc.identifier.eissn1991-7120-
dc.identifier.isiWOS:000328283100008-
dc.identifier.issnl1815-2406-

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