Local refinement of simplicial grids based on the skeleton

Abstract

In this paper we present a novel approach to the development of a class of local simplicial refinement strategies. The algorithm in two dimensions first subdivides certain edges. Then each triangle, if refined, is subdivided in two, three or four subelements depending on the previous division of its edges. Similarly, in three dimensions the algorithm begins by subdividing the two-dimensional triangulation composed by the faces of the tetrahedra (the skeleton) and then subdividing each tetrahedron in a compatible manner with the division of the faces. The complexity of the algorithm is linear in the number of added nodes. The algorithm is fully automatic and has been implemented to achieve global as well as local refinements. The numerical results obtained appear to confirm that the measure of degeneracy of subtetrahedra is bounded, and converges asymptotically to a fixed value when the refinement proceeds.