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

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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.

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