On error indicators for optimizing parameters in stabilized methods

• ID: 2791, RIV: 10404472
• ISSN: 1019-7168, ISBN: not specified
• source: Advances in Computational Mathematics
• keywords: convection-dominated problems; error indicators; parameter optimization; stabilized methods
• authors: Petr Knobloch, Petr Lukáš, Pavel Šolín
• authors from KNM: Lukáš Petr, Knobloch Petr

Abstract

Numerical solution of convection-dominated problems requires special techniques to suppress spurious oscillations in approximate solutions. Often, stabilized methods are applied which involve user-chosen parameters. These parameters significantly influence the quality of the solution but their optimal choice is usually not known. One possibility is to define them in an adaptive way by minimizing an error indicator characterizing the quality of the approximate solution. A non-trivial requirement on the error indicator is that its minimization with respect to the stabilization parameters should suppress spurious oscillations without smearing layers. In this paper, a new error indicator is introduced and its suitability is tested on two newly proposed benchmark problems for which previously proposed indicators do not provide satisfactory results.