Interpolation of non-smooth functions on anisotropic finite element meshes

• Main Author: Apel, Th.
• Other Authors: TU Chemnitz, SFB 393
• Format: Others
• Language: English
• Published: Universitätsbibliothek Chemnitz 1998
• Subjects: anisotropic weighted Sobolev spaces; local interpolation error; estimates.; MSC 35A40; MSC 35J05; MSC 65N30; MSC 35B65; ddc:510
• Online Access: http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199801341; http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199801341; http://www.qucosa.de/fileadmin/data/qucosa/documents/4213/data/b006.pdf; http://www.qucosa.de/fileadmin/data/qucosa/documents/4213/data/b006.ps; http://www.qucosa.de/fileadmin/data/qucosa/documents/4213/19980134.txt

In this paper, several modifications of the quasi-interpolation operator of Scott and Zhang (Math. Comp. 54(1990)190, 483--493) are discussed. The modified operators are defined for non-smooth functions and are suited for the 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.