Shishkin mesh simulation: A new stabilization technique for convection–diffusion problems

A new stabilization procedure is presented. It is based on a simulation of the interaction between the coarse and fine parts of a Shishkin mesh, but can be applied on coarse and irregular meshes and on domains with nontrivial geometries. The technique, which does not require adjusting any parameter, can be applied to different stabilized and non stabilized methods. Numerical experiments show it to obtain oscillation-free approximations on problems with boundary and internal layers, on uniform and nonuniform meshes and on domains with curved boundaries.

► A parameter-free stabilization procedure for convection–diffusion problems is proposed.
► It is applicable to a wide range of stabilized and non stabilized methods.
► Numerical experiments show it produces oscillation-free approximations on problems with boundary and internal layers.
► Numerical experiments suggests it outperforms most of stabilized methods available today.