Propagation Path Properties in Iterative Longest-Edge Refinement

In this work we investigate the refinement propagation process in longest-edge based local refinement algorithms for unstructured meshes of triangles. The conformity neighborhood of a triangle, the set of additional triangles that is needed to be refined to ensure mesh conformity is introduced to define the propagation path. We prove that asymptotically the propagation path extends on average to a few neighbor adjacent triangles. We also include numerical evidence which is in complete agreement with the theoretical study reported.