Grading of Triangulations Generated by Bisection

2023/05/09 by Lars Diening, Johannes Storn, Diening, Lars +3 · 2 citations
Computer Science · Mathematics · #65M15 #65N12 #65N15 #65N50 #Complexity and Algorithms in Graphs #Computational Geometry and Mesh Generation #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2305.05742

openalex publication_date 2023/05/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

For triangulations generated by the adaptive bisection algorithm by Maubach and Traxler we prove existence of a regularized mesh function with grading two. This sharpens previous results in two dimensions for the newest vertex bisection and generalizes them to arbitrary dimensions. In combination with Diening et al. (2021) this yields H¹-stability of the L²-projection onto Lagrange finite element spaces for all polynomial degrees and dimensions smaller than seven.

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