Three anisotropic benchmark problems for adaptive finite element methods

0438689 - ÚT 2015 RIV US eng J - Článek v odborném periodiku
Šolín, Pavel - Čertík, O. - Korous, L.
Three anisotropic benchmark problems for adaptive finite element methods.
Applied Mathematics and Computation. Roč. 219, č. 13 (2013), s. 7286-7295. ISSN 0096-3003. E-ISSN 1873-5649
Grant CEP: GA AV ČR IAA100760702
Institucionální podpora: RVO:61388998
Klíčová slova: benchmark problem * anisotropic solution * boundary layer
Kód oboru RIV: BA - Obecná matematika
Impakt faktor: 1.600, rok: 2013

In this paper we provide three benchmark problems with known exact solutions that can be used to assess the ability of adaptive finite element algorithms to handle anisotropically-behaved solutions. The first one is a Poisson equation with a smooth solution that only changes in one spatial direction. The second one is a singularly-perturbed linear elliptic equation whose solution exhibits a boundary layer, and the last one is a two-equation system that contains a boundary layer in one solution component only. In an appendix we show sample results obtained with the open source library HERMES. (http://hpfem.org/hermes.) (C) 2010 Elsevier Inc. All rights reserved.
Trvalý link: http://hdl.handle.net/11104/0242148