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Optimality of a Gradient Bound for Polyhedral Wachspress Coordinates

  • Michael S. FloaterEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9213)

Abstract

In a recent paper with Gillette and Sukumar an upper bound was derived for the gradients of Wachspress barycentric coordinates in simple convex polyhedra. This bound provides a shape-regularity condition that guarantees the convergence of the associated polyhedral finite element method for second order elliptic problems. In this paper we prove the optimality of the bound using a family of hexahedra that deform a cube into a tetrahedron.

Keywords

Barycentric coordinates Wachspress coordinates polyhedral finite element method 

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of OsloOsloNorway

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