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Long Chen and Pengtao Sun and Jinchao Xu. Multilevel Homotopic Adaptive Finite Element Methods for Convection Dominated Problems. The Proceedings for 15th Conferences for Domain Decomposition Methods, Lecture Notes in Computational Science and Engineering 40:459--468, 2004.

Chen.L%3BSun.P%3BXu.J2004.pdf

ABSTRACT: A multilevel homotopic adaptive methods is presented in this paper for convection dominated problems. By the homotopy method with respect to the diffusion parameter, the grid 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.