Conformal Refinement of Unstructured Quadrilateral Meshes

A multilevel adaptive refinement technique is presented for unstructured quadrilateral meshes in which the mesh is kept conformal at all times. This means that the refined mesh, like the original, is formed of only quadrilateral elements that intersect strictly along edges or at vertices, i.e., vertices of one quadrilateral element do not lie in an edge of another quadrilateral. Elements are refined using templates based on 1:3 refinement of edges. It is demonstrated that by careful design of the refinement and coarsening strategy, high quality elements can be maintained in the refined mesh. The method is demonstrated on a number of examples with dynamically changing refinement regions.