Interpolation of non-smooth functions on anisotropic finite element meshes
TU Chemnitz, Fak. f. Mathematik,
09107 Chemnitz, Germany. email@example.com.
Revised: 3 April 1998
Revised: 26 March 1999
In this paper, several modifications of the quasi-interpolation operator of Scott and Zhang  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.
Mathematics Subject Classification: 65D05 / 65N30 / 65N50
Key words: Anisotropic finite elements / interpolation error estimate / quasi-interpolation / non-smooth functions / edge singularity / reaction diffusion problem.
© EDP Sciences, SMAI, 1999