The 4-triangles longest-side partition of triangles and linear refinement algorithms
Mathematics of Computation
Complexity of the bisection method
Theoretical Computer Science
Lepp-bisection algorithms, applications and mathematical properties
Applied Numerical Mathematics
The propagation problem in longest-edge refinement
Finite Elements in Analysis and Design
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Longest-edge refinement algorithms were designed to iteratively refine the mesh for finite-element applications by maintaining mesh quality (assuring a bound on the smallest angle). In this paper we improve geometrical results on longest-edge refinement algorithms and provide precise bounds on the refinement propagation. We prove that the iterative application of the algorithm gradually reduces the average extent of the propagation per target triangle, tending to affect only two triangles. We also include empirical results which are in complete agreement with the theory.