Mixed finite element methods for nonlinear elliptic problems: The h-p version

Miyoung Lee; Fabio A. Milner

doi:10.1016/S0377-0427(97)00121-0

Mixed finite element methods for nonlinear elliptic problems: The h-p version

Miyoung Lee, Fabio A. Milner

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

6 Scopus citations

Abstract

Mixed finite element methods for strongly nonlinear second order elliptic problems are proposed and analyzed. Existence and uniqueness of the approximate solution are demonstrated using a fixed point argument. Convergence and stability of the method are proved both with respect to mesh refinement and increase of the degree of the approximating polynomials. The analysis is carried out in detail using Raviart-Thomas-Nedelec spaces as an example. Numerical results for minimal surface problems are obtained using Brezzi-Douglas-Marini spaces. Graphs of the approximate solutions are presented for two different problems.

Original language	English (US)
Pages (from-to)	239-261
Number of pages	23
Journal	Journal of Computational and Applied Mathematics
Volume	85
Issue number	2
DOIs	https://doi.org/10.1016/S0377-0427(97)00121-0
State	Published - Nov 12 1997
Externally published	Yes

Keywords

BDM space
Minimal surfaces
Mixed method
Nonlinear elliptic problem

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/S0377-0427(97)00121-0

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title = "Mixed finite element methods for nonlinear elliptic problems: The h-p version",

abstract = "Mixed finite element methods for strongly nonlinear second order elliptic problems are proposed and analyzed. Existence and uniqueness of the approximate solution are demonstrated using a fixed point argument. Convergence and stability of the method are proved both with respect to mesh refinement and increase of the degree of the approximating polynomials. The analysis is carried out in detail using Raviart-Thomas-Nedelec spaces as an example. Numerical results for minimal surface problems are obtained using Brezzi-Douglas-Marini spaces. Graphs of the approximate solutions are presented for two different problems.",

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author = "Miyoung Lee and Milner, {Fabio A.}",

year = "1997",

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TY - JOUR

T1 - Mixed finite element methods for nonlinear elliptic problems

T2 - The h-p version

AU - Lee, Miyoung

AU - Milner, Fabio A.

PY - 1997/11/12

Y1 - 1997/11/12

N2 - Mixed finite element methods for strongly nonlinear second order elliptic problems are proposed and analyzed. Existence and uniqueness of the approximate solution are demonstrated using a fixed point argument. Convergence and stability of the method are proved both with respect to mesh refinement and increase of the degree of the approximating polynomials. The analysis is carried out in detail using Raviart-Thomas-Nedelec spaces as an example. Numerical results for minimal surface problems are obtained using Brezzi-Douglas-Marini spaces. Graphs of the approximate solutions are presented for two different problems.

AB - Mixed finite element methods for strongly nonlinear second order elliptic problems are proposed and analyzed. Existence and uniqueness of the approximate solution are demonstrated using a fixed point argument. Convergence and stability of the method are proved both with respect to mesh refinement and increase of the degree of the approximating polynomials. The analysis is carried out in detail using Raviart-Thomas-Nedelec spaces as an example. Numerical results for minimal surface problems are obtained using Brezzi-Douglas-Marini spaces. Graphs of the approximate solutions are presented for two different problems.

KW - BDM space

KW - Minimal surfaces

KW - Mixed method

KW - Nonlinear elliptic problem

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DO - 10.1016/S0377-0427(97)00121-0

M3 - Article

AN - SCOPUS:0031274106

VL - 85

SP - 239

EP - 261

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

SN - 0377-0427

IS - 2

ER -

Mixed finite element methods for nonlinear elliptic problems: The h-p version

Abstract

Keywords

ASJC Scopus subject areas

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