Superconvergence of the Galerkin iterates for integral equations of the second kind. (English) Zbl 0575.65131

The authors apply Galerkin approximation methods to multidimensional integral equations of the second kind and obtain error estimates in terms of Sobolev norms \(W^ s_ p\) with particular reference to the case \(p\neq 2\). The integral operators involved include those which arise in the boundary integral approach to Laplace’s equation defined for a bounded domain enclosed by a smooth boundary.
Reviewer: D.A.Quinney


65R20 Numerical methods for integral equations
45B05 Fredholm integral equations
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation