On adaptive grid refinement in the presence of internal or boundary layers

Abstract

We propose an anisotropic refinement strategy which is specially designed for the efficient numerical resulution of internal and boundary layers. This strategy is based on the directed refinement of single triangles together with adaptive multilevel grid orientation. Compared to usual methods, the new anisotropic refinement ends up in more stable and more accurate solutions at much less computational cost. This is demonstrated by several numerical examples.