A Patched Mesh Method for Singularly perturbed Reaction-Diffusion Equations

A singularly perturbed elliptic problem of reaction-diffusion type is examined. The solution is decomposed into a sum of a regular component, boundary layer components and corner layer components. Numerical approximations are generated separately for each of these components. These approximations are patched together to form a global approximation to the solution of the continuous problem. An asymptotic error bound in the pointwise maximum norm is established; whose dependence on the values of the singular perturbation parameter is explicitly identified. Numerical results are presented to illustrate the performance of the numerical method.