Adaptive refinement of unstructured finite-element meshes

The finite-element method used in conjunction with adaptive mesh refinement algorithms can be an efficient tool in many scientific and engineering applications. In this paper we review algorithms for the adaptive refinement of unstructured simplicial meshes (triangulations and tetrahedralizations). We discuss bounds on the quality of the meshes resulting from these refinement algorithms. Unrefinement and refinement along curved surfaces are also discussed. Finally, we give an overview of recent developments in parallel refinement algorithms.