ESAIM: Mathematical Modelling and Numerical Analysis

Table of Contents - November 1999 - Volume 33, Issue 06  

Research Article

Interpolation of non-smooth functions on anisotropic finite element meshes

Apel, Thomas

TU Chemnitz, Fak. f. Mathematik, 09107 Chemnitz, Germany. apel@mathematik.tu-chemnitz.de.

Abstract

In this paper, several modifications of the quasi-interpolation operator of Scott and Zhang [30] are discussed. The modified operators are defined for non-smooth functions and are suited for application on anisotropic meshes. The anisotropy of the elements is reflected in the local stability and approximation error estimates. As an application, an example is considered where anisotropic finite element meshes are appropriate, namely the Poisson problem in domains with edges.

(Received October 9 1997)

(Revised April 3 1998)

(Revised March 26 1999)

(Online publication August 15 2002)

Key Words:

  • Anisotropic finite elements;
  • interpolation error estimate;
  • quasi-interpolation;
  • non-smooth functions;
  • edge singularity;
  • reaction diffusion problem.

Mathematics Subject Classification:

  • 65D05;
  • 65N30;
  • 65N50