Parameter uniform numerical methods for singularly perturbed elliptic problems with parabolic boundary layers (Q952785)

The authors provide parameter-uniform numerical methods for singularly perturbed elliptic boundary-value problems with parabolic boundary layers. A priori bounds on the solution and its derivatives are obtained using a suitable decomposition of the solution into smooth and singular components. The domain is discretized by piecewise-uniform meshes. The numerical scheme consists of classical finite difference operators on the piecewise-uniform meshes. First-order (up to logarithmic factor) parameter-uniform convergence results of the numerical approximations are derived.