Published

Multilevel homotopic adaptive finite element methods for convection dominated problems

Long Chen, Pengtao Sun and Jinchao Xu

In The Proceedings for 15th Conferences for Domain Decomposition Methods, Lecture Notes in Computational Science and Engineering 40, pages 459-468. Springer, 2004.

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Abstract: 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.