Interior Estimates for the Wavelet Galerkin Method

S. Bertoluzza

In this paper we derive an interior estimate for the Galerkin method with wavelet-type basis. Such an estimate follows from interior Galerkin equations which are common to a class of methods used in the solution of elliptic boundary value problems. We show that the error in an interior domain D can be estimated with the best order of accuracy possible, provided the solution u is sufficiently regular in a slightly larger domain, and that an estimate of the same order exists for the error in a weaker norm (measuring the effects from outside the domain). Examples of the application of such an estimate are given for different problems.

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