Daniel Loghin : January 23, 2003

Stopping criteria for iterations in finite element methods.

Abstract

Finite element methods form an important source of large, sparse linear systems. They also provide natural (physical) norms in which to measure convergence. However, in general iterative solvers use stopping criteria based on Euclidean norms which give no indication on convergence of quantities relevant to the problem.

In the case of symmetric problems this issue has been addressed in the work of Golub, Meurant, Strakos, who suggest ways to compute the (so-called) energy-norm of the error in CG iterations. Mario Arioli later used these results in the context of finite element problems.

I will talk about recent work with Mario where these ideas are extended to the case of nonsymmetric problems. In particular, I will describe how we address the issue of estimating the same energy-norm of the error (as provided by the finite element context) for GMRES.