Interior estimates for the wavelet Galerkin method

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 Omega(0) can be estimated with the best order of accuracy possible, provided the solution ii 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 Omega(0)). Examples of the application of such an estimate are given for different problems.