We consider the model Dirichlet problem for Poisson's equation on a plane polygonal convex domain Ω with data f in a space smoother than L2. The regularity and the critical case of the problem depend on the measure of the maximum angle of the domain. Interpolation theory and multi-level theory are used to obtain estimates for the critical case. As a consequence, sharp error estimates for the corresponding discrete problem are proved. Some classical shift estimates are also proved using the powerful tools of interpolation theory and multilevel approximation theory. The results can be extended to a large class of elliptic boundary value problems.
|Original language||English (US)|
|Number of pages||20|
|Journal||Journal of Numerical Mathematics|
|State||Published - Jul 21 2003|
Bibliographical noteGenerated from Scopus record by KAUST IRTS on 2023-02-15
ASJC Scopus subject areas
- Computational Mathematics