A Bernstein-Bezier Sufficient Condition for Invertibility of Polynomial Mapping Functions
Stephen Vavasis
TL;DR
This paper introduces a new sufficient condition based on Bernstein-Bézier form analysis to determine the invertibility of polynomial mapping functions, especially useful in finite element analysis with curved meshes.
Contribution
It presents a novel Bernstein-Bézier based criterion for polynomial invertibility applicable to curved mesh finite element methods.
Findings
Provides a practical criterion for invertibility verification.
Applicable to polynomial mappings on cubes and simplices.
Enhances finite element analysis with curved geometries.
Abstract
We propose a sufficient condition for invertibility of a polynomial mapping function defined on a cube or simplex. This condition is applicable to finite element analysis using curved meshes. The sufficient condition is based on an analysis of the Bernstein-B\'ezier form of the columns of the derivative.
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Taxonomy
TopicsAdvanced Numerical Analysis Techniques · Advanced Numerical Methods in Computational Mathematics · Computational Geometry and Mesh Generation