A mixed boundary value problem for a singularly perturbed reaction-diffusion equation in an L-shaped domain

A mixed boundary value problem for a singularly perturbed reaction-diffusion equation in an L-shaped domain is considered for when the solution has singularities at the corners of the domain. The densification of the Shishkin mesh near the inner corner where different boundary conditions meet is such that the solution obtained by the classical five-point difference scheme converges to the solution of the initial problem in the mesh norm L ∞ h uniformly with respect to the small parameter with almost second order, i. e., as a smooth solution. Numerical analysis confirms the theoretical result. © 2012 Allerton Press, Inc.