We study the extrapolation method for the numerical solution of elliptic boundary value problems on corner domains. Most papers on the extrapolation method for solving differential equations require smoothness assumptions on exact solutions, which do not hold for boundary value problems on corner domains. We conjecture that asymptotic error expansions exist as long as there is enough smoothness on the input data except the domain. This is confirmed by our theoretical result on asymptotic error expansions for model problems on a rectangle. Numerical examples suggest that similar results hold for problems on more general corner domains, although it seems very difficult to prove them.
|Number of pages||15|
|Journal||Applied Mathematics and Computation|
|Publication status||Published - Apr 1997|
Scopus Subject Areas
- Computational Mathematics
- Applied Mathematics