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

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

ID: 2617, RIV: 10104793
ISSN: 0045-7825, ISBN: not specified
source: Computer Methods in Applied Mechanics and Engineering
keywords: stabilized finite element methods; parameter optimization; SUPG method
authors: Volker John, Petr Knobloch, Simona B. Savescu
authors from KNM: Knobloch Petr

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.