Mesh and Solver Co-adaptation in Finite Element Methods for Anisotropic Problems

Mesh generation and algebraic solver are two important aspects of the finite element methodology. In this article, we are concerned with the joint adaptation of the anisotropic triangular mesh and the iterative algebraic solver. Using generic numerical examples pertaining to the accurate and efficient finite element solution of some anisotropic problems, we hereby demonstrate that the processes of geometric mesh adaptation and the algebraic solver construction should be adapted simultaneously. We also propose some techniques applicable to the co-adaptation of both anisotropic meshes and linear solvers. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 21: 859–874, 2005