INVESTIGADORES
LOMBARDI Ariel Luis
artículos
Título:
Error Estimates on Anisotropic $Q_1$ Elements for Functions in Weighted Sobolev Spaces
Autor/es:
RICARDO G. DURÁN; ARIEL L. LOMBARDI
Revista:
MATHEMATICS OF COMPUTATION
Editorial:
American Mathematical Society
Referencias:
Lugar: Providence; Año: 2005 vol. 74 p. 1679 - 1706
ISSN:
0025-5718
Resumen:
In this paper we prove error estimates for a piecewise $Q_1$ average interpolation on anisotropic rectangular elements, i.e., rectangles with sides of di®erent orders, in two and three dimensions. Our error estimates are valid under the condition that neighboring elements have comparable size. This is a very mild assumption that includes more general meshes than those allowed in previous papers. In particular, strong anisotropic meshes arising naturally in the approximation of problems with boundary layers fall under our hypotheses. Moreover, we generalize the error estimates allowing on the right hand side some weighted Sobolev norms. This extension is of interest in singularly perturbed problems. Finally, we consider the approximation of functions vanishing on the boundary by finite element functions with the same property, a point that was not considered in previous papers on average interpolations for anisotropic elements. As an application we consider the approximation of a singularly perturbed reaction-diffusion equation and show that, as a consequence of our results, almost optimal order error estimates in the energy norm, valid uniformly in the perturbation parameter, can be obtained.