Parameter-uniform numerical method for singularly perturbed convection-diffusion problem on a circular domain (Q1683215)

This article studies the numerical solution of singularly perturbed linear elliptic boundary value problems in a circular domain. The solution is decomposed into regular and singular components, bounds on the partial derivatives of these components are obtained. The domain is discretized by using the piecewise-uniform Shishkin meshes, and the elliptic partial differential equation is approximated by a classical upwind finite difference scheme. First-order parameter-uniform error estimates are established. Numerical experiments are carried out to verify the theoretical estimates.