Anisotropic mesh construction and error estimation in the finite element method

Gerd Kunert

AutorIn: Gerd Kunert
Titel: Anisotropic mesh construction and error estimation in the finite element method
Zitierfähige Url:: https://nbn-resolving.org/urn:nbn:de:bsz:ch1-200000033
Abstract (EN): In an anisotropic adaptive finite element algorithm one usually needs an error estimator that yields the error size but also the stretching directions and stretching ratios of the elements of a (quasi) optimal anisotropic mesh. However the last two ingredients can not be extracted from any of the known anisotropic a posteriori error estimators. Therefore a heuristic approach is pursued here, namely, the desired information is provided by the so-called Hessian strategy. This strategy produces favourable anisotropic meshes which result in a small discretization error. The focus of this paper is on error estimation on anisotropic meshes. It is known that such error estimation is reliable and efficient only if the anisotropic mesh is aligned with the anisotropic solution. The main result here is that the Hessian strategy produces anisotropic meshes that show the required alignment with the anisotropic solution. The corresponding inequalities are proven, and the underlying heuristic assumptions are given in a stringent yet general form. Hence the analysis provides further inside into a particular aspect of anisotropic error estimation.
Freie Schlagwörter: adaptive algorithm,; finite element,; anisotropic mesh,; anisotropic function,; error estimation,; Hessian
Klassifikation (DDC): 510
Verlag: Technische Universität Chemnitz, Chemnitz
URN Qucosa: urn:nbn:de:bsz:ch1-200000033
Veröffentlichungsdatum Qucosa: 13.01.2000
Dokumenttyp: Preprint
Sprache des Dokumentes: Englisch

Nutzungshinweise für die digitalen Objekte in Qucosa