Generalized multiscale finite element methods. nonlinear elliptic equations

Handle URI:
http://hdl.handle.net/10754/562555
Title:
Generalized multiscale finite element methods. nonlinear elliptic equations
Authors:
Efendiev, Yalchin R. ( 0000-0001-9626-303X ) ; Galvis, Juan; Li, Guanglian; Presho, Michael
Abstract:
In 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.
KAUST Department:
Numerical Porous Media SRI Center (NumPor); Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Publisher:
Global Science Press
Journal:
Communications in Computational Physics
Issue Date:
2013
DOI:
10.4208/cicp.020313.041013a
Type:
Article
ISSN:
18152406
Sponsors:
Y. Efendiev's work is partially supported by the DOE and NSF (DMS 0934837 and DMS 0811180). J. Galvis would like to acknowledge partial support from DOE. This publication is based in part on work supported by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorEfendiev, Yalchin R.en
dc.contributor.authorGalvis, Juanen
dc.contributor.authorLi, Guanglianen
dc.contributor.authorPresho, Michaelen
dc.date.accessioned2015-08-03T10:42:31Zen
dc.date.available2015-08-03T10:42:31Zen
dc.date.issued2013en
dc.identifier.issn18152406en
dc.identifier.doi10.4208/cicp.020313.041013aen
dc.identifier.urihttp://hdl.handle.net/10754/562555en
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.en
dc.description.sponsorshipY. Efendiev's work is partially supported by the DOE and NSF (DMS 0934837 and DMS 0811180). J. Galvis would like to acknowledge partial support from DOE. This publication is based in part on work supported by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).en
dc.publisherGlobal Science Pressen
dc.subjectGeneralized multiscale finite element methoden
dc.subjectHigh-contrasten
dc.subjectNonlinear equationsen
dc.titleGeneralized multiscale finite element methods. nonlinear elliptic equationsen
dc.typeArticleen
dc.contributor.departmentNumerical Porous Media SRI Center (NumPor)en
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalCommunications in Computational Physicsen
dc.contributor.institutionDepartment of Mathematics, Institute for Scientific Computation (ISC), Texas AandM University, College Station, TX 77843, United Statesen
dc.contributor.institutionDepartamento de Mateḿaticas, Universidad Nacional de Colombia, Bogot́a D.C, Colombiaen
kaust.authorEfendiev, Yalchin R.en
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.