TY - JOUR
T1 - Generalized multiscale finite element methods. nonlinear elliptic equations
AU - Efendiev, Yalchin R.
AU - Galvis, Juan
AU - Li, Guanglian
AU - Presho, Michael
N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: 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).
PY - 2015/6/3
Y1 - 2015/6/3
N2 - 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.
AB - 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.
UR - http://hdl.handle.net/10754/562555
UR - https://www.cambridge.org/core/product/identifier/S1815240600005107/type/journal_article
UR - http://www.scopus.com/inward/record.url?scp=84892383543&partnerID=8YFLogxK
U2 - 10.4208/cicp.020313.041013a
DO - 10.4208/cicp.020313.041013a
M3 - Article
SN - 1815-2406
VL - 15
SP - 733
EP - 755
JO - Communications in Computational Physics
JF - Communications in Computational Physics
IS - 3
ER -