A Note on the Shape Regularity of Worsey-Farin Splits
Sining Gong, Johnny Guzm\'an, Michael Neilan
TL;DR
This paper proves that three-dimensional Worsey-Farin refinements maintain the shape-regularity of their original triangulations, ensuring stable and predictable mesh quality in finite element methods.
Contribution
It establishes that Worsey-Farin splits in 3D preserve shape-regularity, a property crucial for numerical stability in mesh refinement.
Findings
Worsey-Farin refinements inherit shape-regularity
Ensures stable mesh quality in 3D finite element meshes
Supports reliable adaptive mesh refinement processes
Abstract
We prove three-dimensional Worsey-Farin refinements inherit their parent triangulations' shape-regularity.
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Taxonomy
TopicsComputational Geometry and Mesh Generation · Advanced Combinatorial Mathematics · Advanced Numerical Analysis Techniques