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

Dongho Kim, Eun-Jae Park

Research output: Contribution to journalArticle

12 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 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.

Original languageEnglish
Pages (from-to)1186-1207
Number of pages22
JournalSIAM Journal on Numerical Analysis
Volume48
Issue number3
DOIs
Publication statusPublished - 2010 Sep 1

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Second-order Elliptic Problems
A Posteriori Error Estimators
A Priori Error Estimates
Nonlinear Elliptic Equations
Mixed Finite Element Method
Mixed Finite Elements
Finite Element Approximation
Approximate Solution
Existence and Uniqueness
Nonlinearity
Gradient
Estimator
Norm
Finite element method
Numerical Examples

All Science Journal Classification (ASJC) codes

  • Numerical Analysis

Cite this

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A priori and a posteriori analysis of mixed finite element methods for nonlinear elliptic equations. / Kim, Dongho; Park, Eun-Jae.

In: SIAM Journal on Numerical Analysis, Vol. 48, No. 3, 01.09.2010, p. 1186-1207.

Research output: Contribution to journalArticle

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