Approximation Theory in Jacobi-weighted Spaces
             and Its Application to the h-p FEM

                            Benqi Guo
                   Department of Mathematics
                 University of Manitoba, Canada

Abstract:  Approximation to functions in the Jacobi-weighted Sobolev and Besov
spaces are analyzed in uniform and robust way for all dimensions. In the
framework of these spaces,  the approximability  of singular functions,
including the upper and lower bounds of approximation error,  is derived.
The approximability of smooth and singular solutions are applied to the h-p
FEM, which yields the optimal convergence of the h-p FEM for elliptic problems
on polygonal domains.