Application of the over-set grid technique to a model singular perturbation problem
A 2D model problem for the stationary convection-diffusion equation is considered (which may become a benchmark problem due to its simple description and the rather complicated solution behaviour). The authors propose to use over-set grids, i.e. several rectangular grids set above each other (possibly turned against each other), and to discretize the problem by central differences. Whereas the total number of grid points was kept constant, the grid spacing is adapted (using the known asymptotic behaviour of the solution in its different parts); moreover, a priority ranking for the different over-set grids is shown to be important. The more sophisticated grids improve the solution essentially but do not lead to \(\epsilon\)-uniform convergence.
scientific article; zbMATH DE number 1582207