2 Douglas N . Arnold ,
نویسنده
چکیده
We consider the approximation properties of finite element spaces on quadrilateral meshes. The finite element spaces are constructed starting with a given finite dimensional space of functions on a square reference element, which is then transformed to a space of functions on each convex quadrilateral element via a bilinear isomorphism of the square onto the element. It is known that for affine isomorphisms, a necessary and sufficient condition for approximation of order r + 1 in L and order r in H is that the given space of functions on the reference element contain all polynomial functions of total degree at most r. In the case of bilinear isomorphisms, it is known that the same estimates hold if the function space contains all polynomial functions of separate degree r. We show, by means of a counterexample, that this latter condition is also necessary. As applications we demonstrate degradation of the convergence order on quadrilateral meshes as compared to rectangular meshes for serendipity finite elements and for various mixed and nonconforming finite elements.
منابع مشابه
Complejos Diferenciales Y Estabilidad Numérica
Este es el texto de la conferencia pronunciada el d́ıa 24 de agosto de 2002 por el profesor Douglas N. Arnold ante el plenario del Congreso Internacional de Matemáticos que tuvo lugar en Peḱın, China, del 20 al 28 de agosto de 2002. La Gaceta de la RSME quiere agradecer a la Sociedad Matemática China su permiso para la presente traducción y publicación y al profesor Arnold por su interés y super...
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• Mixed methods for elastodynamics with weak symmetry. • Mixed finite elements for elasticity on quadrilateral meshes. • Finite element differential forms on curvilinear cubic meshes and their approximation properties. Numer. • Nonconforming tetrahedral mixed finite elements for elasticity. • Mixed finite element approximation of the vector Laplacian with Dirichlet boundary conditions. Math. • ...
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Douglas N. Arnold, ∗ Guy David, † David Jerison, ‡ Svitlana Mayboroda, § and Marcel Filoche ¶ School of Mathematics, University of Minnesota, Minneapolis, MN, USA Univ Paris-Sud, Laboratoire de Mathématiques, CNRS, UMR 8658 Orsay, F-91405∗∗ Mathematics Department, Massachusetts Institute of Technology, Boston, MA, USA Physique de la Matière Condensée, Ecole Polytechnique, CNRS, Palaiseau, Franc...
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The TSNLP project is funded by the CEC and started on 1 December 1993 with a duration of 23 months. We would like to thank our partners in the project: Dominique Estival, Kirsten Falkedal and Sabine Lehmann at ISSCO, Geneva, Eva Dauphin and Veronika Lux and Sylvie Regnier-Prost at Aerospatiale, Paris, and Judith Klein, Klaus Netter and Stephan Oepen at DFKI in Saarbr ucken, Germany. Lorna Balk...
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