Adaptive computation of parameters in stabilized methods for convection-diffusion problems

• ID: 2600, RIV: 10132920
• ISSN: not specified, ISBN: 978-3-642-33133-6
• source: Numerical Mathematics and Advanced Applications 2011
• keywords: adaptive computation of parameters; stabilized methods; convection-diffusion problems
• authors: Volker John, Petr Knobloch
• authors from KNM: Knobloch Petr

Abstract

Stabilized finite element methods for convection-dominated problems contain parameters whose optimal choice is usually not known. This paper presents techniques for computing stabilization parameters in an adaptive way by minimizing a target functional characterizing the quality of the approximate solution. This leads to a constrained nonlinear optimization problem. Numerical results obtained for various target functionals are presented. They demonstrate that a posteriori optimization of parameters can significantly improve the quality of solutions obtained using stabilized methods.