INTERIOR ESTIMATES FOR THE WAVELET GALERKIN METHOD

In this paper we derive an interior estimate for the Galerkin method w ith wavelet-type basis, Such an estimate follows from interior Galerki n equations which are common to a class of methods used in the solutio n of elliptic boundary value problems. We show that the error in an in terior domain Omega(0) can be estimated with the best order of accurac y possible, provided the solution ii is sufficiently regular in a slig htly larger domain, and that an estimate of the same order exists for the error in a weaker norm (measuring the effects from outside the dom ain Omega(0)). Examples of the application of such an estimate are giv en for different problems.