A priori and a posteriori analysis of mixed finite element methods for nonlinear elliptic equations

Dongho Kim; Eun Jae Park

doi:10.1137/090747002

A priori and a posteriori analysis of mixed finite element methods for nonlinear elliptic equations

Dongho Kim, Eun Jae Park

Department of Computational Science and Engineering

Research output: Contribution to journal › Article › peer-review

20 Citations (Scopus)

Abstract

We study the mixed finite element approximation of the second order elliptic problem with gradient nonlinearities in two and three space dimensions. Existence and uniqueness of the approximate solution are proved and optimal order a priori error estimates in L^m(Ω) are obtained. Also, reliable and efficient a posteriori error estimators measured in the L ^m(Ω)-norm are derived. Numerical examples are provided to illustrate the performance of the proposed estimator.

Original language	English
Pages (from-to)	1186-1207
Number of pages	22
Journal	SIAM Journal on Numerical Analysis
Volume	48
Issue number	3
DOIs	https://doi.org/10.1137/090747002
Publication status	Published - 2010

All Science Journal Classification (ASJC) codes

Numerical Analysis
Computational Mathematics
Applied Mathematics

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10.1137/090747002

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abstract = "We study the mixed finite element approximation of the second order elliptic problem with gradient nonlinearities in two and three space dimensions. Existence and uniqueness of the approximate solution are proved and optimal order a priori error estimates in Lm(Ω) are obtained. Also, reliable and efficient a posteriori error estimators measured in the L m(Ω)-norm are derived. Numerical examples are provided to illustrate the performance of the proposed estimator.",

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AB - We study the mixed finite element approximation of the second order elliptic problem with gradient nonlinearities in two and three space dimensions. Existence and uniqueness of the approximate solution are proved and optimal order a priori error estimates in Lm(Ω) are obtained. Also, reliable and efficient a posteriori error estimators measured in the L m(Ω)-norm are derived. Numerical examples are provided to illustrate the performance of the proposed estimator.

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A priori and a posteriori analysis of mixed finite element methods for nonlinear elliptic equations

Abstract

All Science Journal Classification (ASJC) codes

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