Mixed finite element methods for nonlinear second-order elliptic problems*

Research output: Contribution to journalArticle

60 Citations (Scopus)

Abstract

Mixed finite element methods are developed to approximate the solution of the Dirichlet problem for the most general quasi-linear second-order elliptic operator in divergence form. Existence and uniqueness of the approximation are proved, and optimal error estimates in L2 are demonstrated for both the scalar and vector functions approximated by the method. Error estimates Newton’s method is presented and analyzed to solve the are nonlinear also derived algebraic in equations. Lq, 2_q_+c.

Original languageEnglish
Pages (from-to)865-885
Number of pages21
JournalSIAM Journal on Numerical Analysis
Volume32
Issue number3
DOIs
Publication statusPublished - 1995 Jan 1

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Second-order Elliptic Problems
Optimal Error Estimates
Mixed Finite Element Method
Linear Order
Elliptic Operator
Newton Methods
Dirichlet Problem
Error Estimates
Divergence
Existence and Uniqueness
Scalar
Finite element method
Newton-Raphson method
Approximation
Form

All Science Journal Classification (ASJC) codes

  • Numerical Analysis

Cite this

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abstract = "Mixed finite element methods are developed to approximate the solution of the Dirichlet problem for the most general quasi-linear second-order elliptic operator in divergence form. Existence and uniqueness of the approximation are proved, and optimal error estimates in L2 are demonstrated for both the scalar and vector functions approximated by the method. Error estimates Newton’s method is presented and analyzed to solve the are nonlinear also derived algebraic in equations. Lq, 2_q_+c.",
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Mixed finite element methods for nonlinear second-order elliptic problems*. / Park, Eun-Jae.

In: SIAM Journal on Numerical Analysis, Vol. 32, No. 3, 01.01.1995, p. 865-885.

Research output: Contribution to journalArticle

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