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

Eun Jae Park

doi:10.1137/0732040

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

Eun Jae Park

Department of Computational Science and Engineering

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

78 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 language	English
Pages (from-to)	865-885
Number of pages	21
Journal	SIAM Journal on Numerical Analysis
Volume	32
Issue number	3
DOIs	https://doi.org/10.1137/0732040
Publication status	Published - 1995

Bibliographical note

Funding Information:
Received by the editors April 20, 1993; accepted for publication (in revised form) December 10, 1993. This work was supported in part by the Purdue Research Foundation. Department of Mathematics, Purdue University, West Lafayette, Indiana 47907-1395. Current address: Dipartimento di Matematica, Universit di Trento, 38050 Povo, Italy (park(C)volterra. science,un+/-tn, it).

Publisher Copyright:
© 1995 Society for Industrial and Applied Mathematics.

All Science Journal Classification (ASJC) codes

Numerical Analysis
Computational Mathematics
Applied Mathematics

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10.1137/0732040

Cite this

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title = "Mixed finite element methods for nonlinear second-order elliptic problems*",

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{\textquoteright}s method is presented and analyzed to solve the are nonlinear also derived algebraic in equations. Lq, 2_q_+c.",

author = "Park, {Eun Jae}",

note = "Funding Information: Received by the editors April 20, 1993; accepted for publication (in revised form) December 10, 1993. This work was supported in part by the Purdue Research Foundation. Department of Mathematics, Purdue University, West Lafayette, Indiana 47907-1395. Current address: Dipartimento di Matematica, Universit di Trento, 38050 Povo, Italy (park(C)volterra. science,un+/-tn, it). Publisher Copyright: {\textcopyright} 1995 Society for Industrial and Applied Mathematics.",

year = "1995",

doi = "10.1137/0732040",

language = "English",

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journal = "SIAM Journal on Numerical Analysis",

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PY - 1995

Y1 - 1995

N2 - 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.

AB - 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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JF - SIAM Journal on Numerical Analysis

IS - 3

ER -

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

Abstract

Bibliographical note

All Science Journal Classification (ASJC) codes

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