Finite Element Methods for Mildly Nonlinear Elliptic Equations and Inequalities

1976 ◽  
pp. 259-262
Author(s):  
J. R. Whiteman
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Nonlinear Elliptic

scholarly journals Generalized Multiscale Finite Element Methods. Nonlinear Elliptic Equations

2014 ◽  
Vol 15 (3) ◽  
pp. 733-755 ◽  
Author(s):  
Yalchin Efendiev ◽  
Juan Galvis ◽  
Guanglian Li ◽  
Michael Presho
Keyword(s):  
Finite Element ◽  
Discontinuous Galerkin ◽  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Problem Formulation ◽  
Nonlinear Elliptic ◽  
Continuous Galerkin ◽  
Previous Solution ◽  
Multiscale Finite Element ◽  
Multiscale Finite Element Methods

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.

A new concept of reduced measure for nonlinear elliptic equations

2004 ◽  
Vol 339 (3) ◽  
pp. 169-174 ◽  
Author(s):  
Haïm Brezis ◽  
Moshe Marcus ◽  
Augusto C. Ponce
Keyword(s):  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Nonlinear Elliptic
Sign in / Sign up

Export Citation Format

Share Document