Grading of triangulations generated by bisection

Diening, Lars; Storn, Johannes; Tscherpel, Tabea

doi:10.1090/mcom/4102

Grading of triangulations generated by bisection
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by Lars Diening, Johannes Storn and Tabea Tscherpel;

Math. Comp.

DOI: https://doi.org/10.1090/mcom/4102

Published electronically: June 13, 2025

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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, Storn, and Tscherpel [SIAM J. Numer. Anal. 59 (2021), pp. 2571–2607] this yields $H^1$-stability of the $L^2$-projection onto Lagrange finite element spaces for all polynomial degrees and dimensions smaller than seven.

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Mathematics of Computation

Grading of triangulations generated by bisection
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Abstract: