AN ERROR EXPANSION FOR CUBATURE WITH AN INTEGRAND WITH HOMOGENEOUS BOUNDARY SINGULARITIES

A common strategy in the numerical integration over an n-dimensional h ypercube or simplex, is to consider a regular subdivision of the integ ration domain into m(n) subdomains and to approximate the integral ove r each subdomain by means of a cubature formula. An asymptotic error e xpansion when m --> infinity is derived in case of an integrand with h omogeneous boundary singularities. The error expansion also copes with the use of different cubature formulas for the boundary subdomains an d for the interior subdomains.