Goal-oriented a posteriori error estimates for transport problems

Dmitri Kuzmin*, Sergey Korotov

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

12 Citations (Scopus)

Abstract

Some aspects of goal-oriented a posteriori error estimation are addressed in the context of steady convection-diffusion equations. The difference between the exact and approximate values of a linear target functional is expressed in terms of integrals that depend on the solutions to the primal and dual problems. Gradient averaging techniques are employed to separate the element residual and diffusive flux errors without introducing jump terms. The dual solution is computed numerically and interpolated using higher-order basis functions. A node-based approach to localization of global errors in the quantities of interest is pursued. A possible violation of Galerkin orthogonality is taken into account. Numerical experiments are performed for centered and upwind-biased approximations of a 1D boundary value problem.

Original languageEnglish
Pages (from-to)1674-1683
Number of pages10
JournalMathematics and Computers in Simulation
Volume80
Issue number8
DOIs
Publication statusPublished - Apr 2010
MoE publication typeA1 Journal article-refereed

Keywords

  • A posteriori error estimates
  • Goal-oriented quantities
  • Mesh adaptation
  • Stationary convection-diffusion equations
  • The finite element method

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