Numerical Studies of Adaptive Finite Element Methods for Two Dimensional Convection-Dominated Problems

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.

• Content Type Journal Article
• DOI 10.1007/s10915-009-9337-6
• Authors
  
  
  • Pengtao Sun, University of Nevada, Las Vegas Department of Mathematical Sciences 4505 Maryland Parkway Las Vegas NV 89154 USA
  • Long Chen, University of California, Irvine Department of Mathematics Irvine CA 92697 USA
  • Jinchao Xu, Pennsylvania State University Department of Mathematics University Park PA 16802 USA
  
  

• Journal Journal of Scientific Computing
• Online ISSN 1573-7691
• Print ISSN 0885-7474

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Original source : http://www.springerlink.com/content/l61j2jk46347t5...