hp Gauss-Legendre Quadrature for Layer Functions

Abstract

. We consider the numerical approximation of integrals involving layer functions, which appear as components in the solution of singularly perturbed boundary value problems. The hp version of the Gauss-Legendre composite quadrature, from [1], is utilized in conjunction with the Spectral Boundary Layer mesh from [2]. We show that the error goes to zero exponentially fast, as the number of Gauss points increases, independently of the singular perturbation parameter. Numerical examples illustrating the theory are also presented.