Anisotropic mesh refinement for finite element methods based on error reduction

Juan C. Aguilar, Jonathan B. Goodman

Research output: Contribution to journalArticlepeer-review


In this paper, we propose an anisotropic adaptive refinement algorithm based on the finite element methods for the numerical solution of partial differential equations. In 2-D, for a given triangular grid and finite element approximating space V, we obtain information on location and direction of refinement by estimating the reduction of the error if a single degree of freedom is added to V. For our model problem the algorithm fits highly stretched triangles along an interior layer, reducing the number of degrees of freedom that a standard h-type isotropic refinement algorithm would use.

Original languageEnglish (US)
Pages (from-to)497-515
Number of pages19
JournalJournal of Computational and Applied Mathematics
Issue number2
StatePublished - Sep 1 2006


  • Adaptive mesh refinement
  • Anisotropic refinement
  • Error estimators
  • Finite elements
  • Triangular grids

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


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