Continuing an earlier work in space dimension one, the aim of this
article is to present, in space dimension two, a novel method to approximate
stiff problems using a combination of (relatively easy) analytical methods and
finite volume discretization. The stiffness is caused by a small parameter in
the equation which introduces ordinary and corner boundary layers along the
boundaries of a two-dimensional rectangle domain. Incorporating in the finite volume space the boundary layer correctors, which are explicitly found by
analysis, the boundary layer singularities are absorbed and thus uniform meshes
can be preferably used. Using the central difference scheme at the volume interfaces,
the proposed scheme finally appears to be an efficient second-order
accurate one.