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Crouzeix-Raviart type finite elements on anisotropic meshes |
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| Authors: | Thomas Apel Serge Nicaise Joachim Schöberl |
| Institution: | TU Chemnitz, Fakult?t für Mathematik, 09107 Chemnitz, Germany; e-mail: na.apel@na-net.ornl.gov, DE Université de Valenciennes et du Hainaut Cambrésis, LIMAV, Institut des Sciences et Techniques de Valenciennes, B.P. 311, 59304 Valenciennes Cedex, France; e-mail: snicaise@univ-valenciennes.fr, FR Johannes Kepler Universit?t Linz, Freist?dterstrasse 313, 4020 Linz, Austria; e-mail: joachim@saturn.sfb013.uni-linz.ac.at, AT |
| Abstract: | Summary. The paper deals with a non-conforming finite element method on a class of anisotropic meshes. The Crouzeix-Raviart element is used on triangles and tetrahedra. For rectangles and prismatic (pentahedral) elements a novel set of trial functions is proposed. Anisotropic local interpolation error estimates are derived for all these types of element and for functions from classical and weighted Sobolev spaces. The consistency error is estimated for a general differential equation under weak regularity assumptions. As a particular application, an example is investigated where anisotropic finite element meshes are appropriate, namely the Poisson problem in domains with edges. A numerical test is described. Received May 19, 1999 / Revised version received February 2, 2000 / Published online February 5, 2001 |
| Keywords: | Mathematics Subject Classification (1991): 65N30 65N15 65N50 65D05 |
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