Guaranteed error bounds for finite element approximations of noncoercive elliptic problems and their applications

Mitsuhiro T. Nakao, Kouji Hashimoto

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

In this paper, we discuss with guaranteed a priori and a posteriori error estimates of finite element approximations for not necessarily coercive linear second order Dirichlet problems. Here, 'guaranteed' means we can get the error bounds in which all constants included are explicitly given or represented as a numerically computable form. Using the invertibility condition of concerning elliptic operator, guaranteed a priori and a posteriori error estimates are formulated. This kind of estimates plays essential and important roles in the numerical verification of solutions for nonlinear elliptic problems. Several numerical examples that confirm the actual effectiveness of the method are presented.

Original languageEnglish
Pages (from-to)106-115
Number of pages10
JournalJournal of Computational and Applied Mathematics
Volume218
Issue number1
DOIs
Publication statusPublished - 2008 Aug 15
Externally publishedYes

Fingerprint

A Posteriori Error Estimates
Finite Element Approximation
Elliptic Problems
Error Bounds
Numerical Verification
Nonlinear Elliptic Problems
Invertibility
Linear Order
Elliptic Operator
Dirichlet Problem
Numerical Examples
Estimate
Form

Keywords

  • Guaranteed a priori and a posteriori error estimates
  • Linear elliptic problem

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics
  • Numerical Analysis

Cite this

Guaranteed error bounds for finite element approximations of noncoercive elliptic problems and their applications. / Nakao, Mitsuhiro T.; Hashimoto, Kouji.

In: Journal of Computational and Applied Mathematics, Vol. 218, No. 1, 15.08.2008, p. 106-115.

Research output: Contribution to journalArticle

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