Abstract: A Wavelet Interpolating Galerkin Method (WIGM) for elliptic partial differential equations,especially in irregular regions,is considered.It is proved that the WIGM produces an approximation with an error no more than C2^-m in the Sobolev space norm.A numerical WIGM algorithm for static electromagnetic field analysis in irregular regions is presented.A symmetric interpolating scaling function is selected as the base function.Its symmetry and relation with average-interpolating scaling function are used to reduce numerical computations.Examples presented demonstrate validity of the algorithm.

Key words: boundary value problem, multiresolution analysis (MRA), wavelet interpolating Galerkin method (WIGM), Sobolev space, external wavelet