EXTRAPOLATION OF NUMERICAL-SOLUTIONS FOR ELLIPTIC PROBLEMS ON CORNER DOMAINS

We study the extrapolation method for the numerical solution of ellipt ic boundary value problems on corner domains. Most papers on the extra polation method for solving differential equations require smoothness assumptions on exact solutions, which do not hold for boundary value p roblems on corner domains. We conjecture that asymptotic error expansi ons exist as long as there is enough smoothness on the input data exce pt the domain. This is confirmed by our theoretical result on asymptot ic error expansions for model problems on a rectangle. Numerical examp les suggest that similar results hold for problems on more general cor ner domains, although it seems very difficult to prove them. (C) Elsev ier Science Inc., 1997.