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

Miyoung Lee, Fabio Milner

Research output: Contribution to journalArticle

5 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)239-261
Number of pages23
JournalJournal of Computational and Applied Mathematics
Volume85
Issue number2
StatePublished - Nov 12 1997
Externally publishedYes

Fingerprint

Hp-version
Nonlinear Elliptic Problems
Mixed Finite Element Method
Approximate Solution
Polynomials
Finite element method
Second-order Elliptic Problems
Mesh Refinement
Minimal surface
Stability and Convergence
Existence and Uniqueness
Fixed point
Numerical Results
Polynomial
Graph in graph theory

Keywords

  • BDM space
  • Minimal surfaces
  • Mixed method
  • Nonlinear elliptic problem

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics
  • Numerical Analysis

Cite this

Mixed finite element methods for nonlinear elliptic problems : The h-p version. / Lee, Miyoung; Milner, Fabio.

In: Journal of Computational and Applied Mathematics, Vol. 85, No. 2, 12.11.1997, p. 239-261.

Research output: Contribution to journalArticle

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