A posteriori error estimates for general numerical methods for Hamilton-Jacobi equations. Part I: The steady state case

Samuel Albert, Bernardo Cockburn, Donald A. French, Todd E. Peterson

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

Abstract

A new upper bound is provided for the L-norm of the difference between the viscosity solution of a model steady state Hamilton-Jacobi equation. u, and any given approximation, v. This upper bound is independent of the method used to compute the approximation v; it depends solely on the values that the residual takes on a subset of the domain which can be easily computed in terms of v. Numerical experiments investigating the sharpness of the a posteriori error estimate are given.

Original languageEnglish (US)
Pages (from-to)49-76
Number of pages28
JournalMathematics of Computation
Volume71
Issue number237
DOIs
StatePublished - 2002

Keywords

  • Error estimates
  • Hamilton-Jacobi

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