Chapter

Domain Decomposition Methods in Science and Engineering

Volume 40 of the series Lecture Notes in Computational Science and Engineering pp 459-468

Multilevel Homotopic Adaptive Finite Element Methods for Convection Dominated Problems

  • Long ChenAffiliated withDepartment of Mathematics, The Pennsylvania State University
  • , Pengtao SunAffiliated withDepartment of Mathematics, The Pennsylvania State University
  • , Jinchao XuAffiliated withDepartment of Mathematics, The Pennsylvania State University

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Summary

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.