Geometric Properties of the Local Refinement in Unstructured Triangular Meshes

In this work we study the propagation problem due to the conformity process in the longestedge based refinement algorithms for triangular unstructured meshes. The geometric properties in study answers the important question of how the size of the triangulation is affected when local refinement is applied. We prove both theoretically and empirically that the propagation of a single triangle refinement asymptotically extends to a few neighbor adjacent triangles. We found the limits of the propagation using two metrics which are related to the Longest-Edge Propagation Path (LEPP). The geometric place where a particular class of triangles, the non terminal triangles, are located within each refined mesh is also investigated and some remarkable properties are presented.