Error estimates for finite element approximations of nonlinear monotone elliptic problems with application to numerical homogenization
Abdulle, Assyr; Huber, Martin Ernst
2016

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Abstract

We consider a finite element method (FEM) with arbitrary polynomial degree for nonlinear monotone elliptic problems. Using a linear elliptic projection, we first give a new short proof of the optimal convergence rate of the FEM in the L2 norm. We then derive optimal a priori error estimates in the H 1 and L2 norm for a FEM with variational crimes due to numerical integration. As an application we derive a priori error estimates for a numerical homogenization method applied to nonlinear monotone elliptic problems.

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Title Error estimates for finite element approximations of nonlinear monotone elliptic problems with application to numerical homogenization
Author(s) Abdulle, Assyr ; Huber, Martin Ernst
Published in Numerical Methods for Partial Differential Equations
Pagination 15
Volume 32
Issue 3
Pages 955-969
Date 2016
Publisher Hoboken, Wiley-Blackwell
ISSN 0749-159X
Keywords
DOI https://doi.org/10.1002/num.22037
Other identifier(s) View record in Web of Science
Laboratories ANMC
Record Appears in Scientific production and competences > SB - School of Basic Sciences > SB Archives > ANMC - Chair of Computational Mathematics and Numerical Analysis
Scientific production and competences > SB - School of Basic Sciences > Mathematics
Work produced at EPFL
Journal Articles
Published
Record creation date 2014-08-22

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