Adaptive stopping criterion for iterative linear solvers combined with anisotropic mesh adaptation, application to convection-dominated problems

Abstract

In this work we propose an automatic adaptive stopping criterion integrated with the anisotropic mesh adaptation procedure, thus requiring no additional computational cost. Using information from this procedure we provide control for the linear solver convergence, stopping the iterative solution when the algebraic error is lower than the estimated discretization error. We apply this framework to steady and unsteady convection–diffusion problems, using a stabilized finite element formulation. The proposed method proves to be an effective cost-free strategy to reduce the number of iterations needed, without spoiling the accuracy of the solution.