Numerical studies of adaptive finite element methods for two dimensional convection-dominated problems

Pengtao Sun, Long Chen, Jinchao Xu

Research output: Contribution to journalArticlepeer-review

22 Scopus citations

Abstract

In this paper, we study the stability and accuracy of adaptive finite element methods for the convection-dominated convection-diffusion-reaction problem in the two-dimension space. Through various numerical examples on a type of layer-adapted grids (Shishkin grids), we show that the mesh adaptivity driven by accuracy alone cannot stabilize the scheme in all cases. Furthermore the numerical approximation is sensitive to the symmetry of the grid in the region where the solution is smooth. On the basis of these two observations, we develop a multilevel-homotopic-adaptive finite element method (MHAFEM) by combining streamline diffusion finite element method, anisotropic mesh adaptation, and the homotopy of the diffusion coefficient. We use numerical experiments to demonstrate that MHAFEM can efficiently capture boundary or interior layers and produce accurate solutions.

Original languageEnglish (US)
Pages (from-to)24-43
Number of pages20
JournalJournal of Scientific Computing
Volume43
Issue number1
DOIs
StatePublished - Apr 1 2010

All Science Journal Classification (ASJC) codes

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • Engineering(all)
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

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