A prototype four-dimensional Galerkin-type integral (Q2503988)

The paper deals with the evaluation of four-dimensional integrals using the Galerkin boundary element method. The author investigates a single prototype example to see whether a proper underlying error expansion for extrapolation exists. He makes use of the four-dimensional product \(m\)-panel midpoint trapezoidal rule for the region \([0,1]^4\) and he finds the asymptotic expansion for the error functional. A numerical example to illustrate how this expansion may be applied in extrapolation quadrature is also presented.