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Estimates for quasipolynomials and the convergence in highest norms of approximation methods of solving elliptic problems in domains with corners. (English) Zbl 0575.65107

Probleme und Methoden der Mathematischen Physik, 8. Tag., Karl-Marx-Stadt 1983, Teubner-Texte Math. 63, 46-52 (1984).
[For the entire collection see Zbl 0539.00019.]
A survey paper on the problem of the title. The non-smooth domains have singular points of conic type. Consequently, the solution cannot be well approximated by polynomials. In this paper the approximate solution is sought as a quasipolynomial in the distance from the singularity. The convergence in higher norms of such hybrid methods is studied by using estimates of Markov type. Typical results are illustrated by examples.
Reviewer: W.Ames

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations

Citations:

Zbl 0539.00019