A posteriori optimization of parameters in stabilized methods for convection-diffusion problems - Part I

Abstract

Stabilized finite element methods for convection-dominated problems require the choice of appropriate stabilization parameters. From numerical analysis, often only their asymptotic values are known.

This paper presents a general framework for optimizing stabilization parameters with respect to the minimization of a target functional. Exemplarily, this framework is applied to the SUPG finite element method and the minimization of a residual-based error estimator, an error indicator, and a functional including the crosswind derivative of the computed solution.

Benefits of the basic approach are demonstrated by means of numerical results.

Keywords

• stabilized finite element methods
• parameter optimization
• SUPG method