Goal-oriented error estimation and adaptivity for the finite element method

J. T. Oden*, Serge Prudhomme

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

280 Scopus citations

Abstract

In this paper, we study a new approach in a posteriori error estimation, in which the numerical error of finite element approximations is estimated in terms of quantities of interest rather than the classical energy norm. These so-called quantities of interest are characterized by linear functionals on the space of functions to where the solution belongs. We present here the theory with respect to a class of elliptic boundary-value problems, and in particular, show how to obtain accurate estimates as well as upper and lower bounds on the error. We also study the new concept of goal-oriented adaptivity, which embodies mesh adaptation procedures designed to control error in specific quantities. Numerical experiments confirm that such procedures greatly accelerate the attainment of local features of the solution to preset accuracies as compared to traditional adaptive schemes based on energy norm error estimates.

Original languageEnglish (US)
Pages (from-to)735-756
Number of pages22
JournalComputers and Mathematics with Applications
Volume41
Issue number5-6
DOIs
StatePublished - Jan 1 2001

ASJC Scopus subject areas

  • Modeling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics

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