Geometric diagram for representing shape quality in mesh refinement. (English) Zbl 1363.65211

Suárez, José P.; Plaza, Ángel; Moreno, Tania

Brandts, J. (ed.) et al., Proceedings of the international conference ‘Applications of mathematics’, Prague, Czech Republic, November 18–21, 2015. In honor of the birthday anniversaries of Ivo Babuška (90), Milan Práger (85), and Emil Vitásek (85). Prague: Czech Academy of Sciences, Institute of Mathematics (ISBN 978-80-85823-65-3). 225-235 (2015).

Summary: We review and discuss a method to normalize triangles by the longest-edge. A geometric diagram is described as a helpful tool for studying and interpreting the quality of triangle shapes during iterative mesh refinements. Modern CAE systems as those implementing the finite element method require such tools for guiding the user about the quality of generated triangulations. In this paper we show that a similar method and corresponding geometric diagram in the three-dimensional case do not exist.
For the entire collection see [Zbl 1329.00187].

MSC:

65N50	Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
65M50	Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65M60	Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs

Keywords:

mesh generation; longest-edge refinement; geometric diagram; mesh regularity; iterative mesh refinements; finite element method