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Polynomial approximation of some singular functions. (English) Zbl 0701.41009

The singularities of the solution of a Poisson equation in a polygonal domain are essentially the distance to a corner, up to a positive but weak power. We prove that the high degree polynomial approximation of such functions is better than the result given by the general theory. This leads to an improvement of the error estimates in some spectral type discretizations.
Reviewer: C.Bernardi

MSC:

41A10 Approximation by polynomials
65N15 Error bounds for boundary value problems involving PDEs
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