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

Pengtao Sun, Long Chen, Jinchao Xu

Research output: Contribution to journalArticle

21 Citations (Scopus)

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

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Adaptive Finite Element Method
Convection
Numerical Study
Grid
Finite element method
Mesh Adaptivity
Streamline Diffusion
Interior Layer
Anisotropic Mesh
Mesh Adaptation
Convection-diffusion
Numerical Approximation
Diffusion Coefficient
Homotopy
Boundary Layer
Convergence of numerical methods
Two Dimensions
Finite Element Method
Numerical Experiment
Symmetry

All Science Journal Classification (ASJC) codes

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

Cite this

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Numerical studies of adaptive finite element methods for two dimensional convection-dominated problems. / Sun, Pengtao; Chen, Long; Xu, Jinchao.

In: Journal of Scientific Computing, Vol. 43, No. 1, 01.04.2010, p. 24-43.

Research output: Contribution to journalArticle

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