Mixed Methods for Nonlinear Second-Order Elliptic Problems in Three Variables

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

Mixed finite element methods for treating the Dirichlet problem for fully nonlinear second-order elliptic operators in divergence form are extended to cover the three-dimensional case. 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 for the pressure variable are also derived in Lq; the result is optimal in order for 2 ≤ q ≤ 6 and less than optimal for 6 < q ≤ +∞. Newton's method can be used to solve the nonlinear algebraic equations.

Original languageEnglish
Pages (from-to)41-57
Number of pages17
JournalNumerical Methods for Partial Differential Equations
Volume12
Issue number1
Publication statusPublished - 1996 Jan 1

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Second-order Elliptic Problems
Mixed Methods
Nonlinear Algebraic Equations
Optimal Error Estimates
Mixed Finite Element Method
Fully Nonlinear
Newton-Raphson method
Elliptic Operator
Nonlinear equations
Newton Methods
Dirichlet Problem
Error Estimates
Divergence
Existence and Uniqueness
Scalar
Cover
Finite element method
Three-dimensional
Approximation
Form

All Science Journal Classification (ASJC) codes

  • Analysis
  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

Cite this

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Mixed Methods for Nonlinear Second-Order Elliptic Problems in Three Variables. / Park, Eun Jae.

In: Numerical Methods for Partial Differential Equations, Vol. 12, No. 1, 01.01.1996, p. 41-57.

Research output: Contribution to journalArticle

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