An automatic adaptive meshing technique for Delaunay triangulations Original Research Article

A new algorithm is described for adaptivity of Delaunay triangulations. It distinguishes between regions of mesh according to whether they are to be refined, unaltered or coarsened. The method automatically identifies nodes of the mesh which are candidates for deletion. For a region to be coarsened, a node deletion process is proposed and it is proved that the resulting triangulation is Delaunay. After coarsening, the mesh retains a high quality for two reasons: the first is because a set of nodes have been used to obtain the coarse mesh, which are equi-distant apart, in some sense defined by the original mesh; the second is because the triangulation is Delaunay. The mesh refinement procedure sub-divides elements into a number of similar elements in the regions to be refined. Two-dimensional examples demonstrate the quality of the mesh after coarsening/refinement.