A local refinement algorithm for the longest‐edge trisection of triangle meshes

In this paper we present a local refinement algorithm based on the longest‐edge trisection of triangles. Local trisection patterns are used to generate a conforming triangulation, depending on the number of non‐conforming nodes per edge presented. We describe the algorithm and provide a study of the efficiency (cost analysis) of the triangulation refinement problem. The algorithm presented, and its associated triangle partition, afford a valid strategy to refine triangular meshes. Some numerical studies are analysed together with examples of applications in the field of mesh refinement.