Work

Generalized Multiscale Finite Element Methods. Nonlinear Elliptic Equations

Year: 2013

Type: article

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.

Source: Communications in Computational Physics

DOI: 10.4208/cicp.020313.041013a

Authors: Yalchin Efendiev, Juan Galvis, Guanglian Li, Michael Presho

Institutions: King Abdullah University of Science and Technology, Texas A&M University, Universidad Nacional de Colombia

Language: English

Topic: Advanced Mathematical Modeling in Engineering

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, U.S. Department of Energy, King Abdullah University of Science and Technology

Awards: G3293193970, G4488310539, Iterative upscaling of fluid flows in nonlinear deformable porous media, G771766363, CMG RESEARCH: Predictive Modeling of Thermally Driven Hydrologic Fluxes for Land and Atmosphere Interactions Across Space and Time Scales