A parameter-uniform numerical method for a singularly perturbed two parameter elliptic problem (Q647426)

The authors study a numerical method for a class of singularly perturbed elliptic problems in a rectangular domain with two singular perturbation parameters. A numerical algorithm based on an upwind finite difference operator and a tensor product of piecewise-uniform Shishkin meshes is analyzed, and the authors establish the parameter-uniform error estimates for the numerical approximation. The main ingredient in the numerical analysis is to derive pointwise bounds on the derivatives (up to third order) of the solution which explicitly identify how these derivatives depend on the singular parameters, and the pointwise bounds are obtained by decomposing the solution into a sum of regular, boundary layer and corner layer components, and controlling these components, respectively.