Multilevel Homotopic Adaptive Finite Element Methods for Convection Dominated Problems

  • Long Chen
  • Pengtao Sun
  • Jinchao Xu
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 40)


A multilevel homotopic adaptive finite element method is presented in this paper for convection dominated problems. By the homotopic method with respect to the diffusion parameter, the grids are iteratively adapted to better approximate the solution. Some new theoretic results and practical techniques for the grid adaptation are presented. Numerical experiments show that a standard finite element scheme based on this properly adapted grid works in a robust and efficient manner.


Hessian Matrix Posteriori Error Interpolation Error Posteriori Error Estimate Adaptive Grid 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Long Chen
    • 1
  • Pengtao Sun
    • 1
  • Jinchao Xu
    • 1
  1. 1.Department of MathematicsThe Pennsylvania State University

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