Numerical solution of a reaction-diffusion elliptic interface problem with strong anisotropy

We consider a singularly perturbed reaction-diffusion elliptic problem in two dimensions (x,y), with strongly anisotropic coefficients and line interface. The second order derivative with respect to x is multiplied by a small parameter epsilon(2). We construct finite volume difference schemes on condensed Shihskin meshes and prove epsilon-uniform convergence in discrete energy and maximum norms. Numerical experiments that agree with the theoretical results are given.