An [formula omitted] finite element method for a two-dimensional singularly perturbed boundary value problem with two small parameters

Abstract

We consider a singularly perturbed boundary value problem, of reaction–convection–diffusion type with two small parameters, and the approximation of its solution by the hp version of the Finite Element Method on the Spectral Boundary Layer mesh. We show that the method converges uniformly, with respect to both singular perturbation parameters, at an exponential rate when the error is measured in the energy norm. Numerical examples illustrating our theoretical findings are also included.