Uniformly convergent difference scheme for singularly perturbed problem of mixed type

A one dimensional singularly perturbed elliptic problem with discontinuous coefficients is considered. The domain under consideration is partitioned into two subdomains. In the first subdomain a convection-diffusion-reaction equation is posed. In the second one we have a pure reaction-diffusion equation. The problem is discretized using an inverse-monotone finite volume method on Shishkin meshes. We establish an almost second-order global pointwise convergence that is uniform with respect to the perturbation parameter. Numerical experiments that support the theoretical results are given.