Recent advances in the construction of polygonal finite element interpolants

  • N. SukumarEmail author
  • E. A. Malsch


This paper is an overview of recent developments in the construction of finite element interpolants, which areC 0-conforming on polygonal domains. In 1975, Wachspress proposed a general method for constructing finite element shape functions on convex polygons. Only recently has renewed interest in such interpolants surfaced in various disciplines including: geometric modeling, computer graphics, and finite element computations. This survey focuses specifically on polygonal shape functions that satisfy the properties of barycentric coordinates: (a) form a partition of unity, and are non-negative; (b) interpolate nodal data (Kronecker-delta property), (c) are linearly complete or satisfy linear precision, and (d) are smooth within the domain. We compare and contrast the construction and properties of various polygonal interpolants—Wachspress basis functions, mean value coordinates, metric coordinate method, natural neighbor-based coordinates, and maximum entropy shape functions. Numerical integration of the Galerkin weak form on polygonal domains is discussed, and the performance of these polygonal interpolants on the patch test is studied.


Shape Function Convex Polygon Voronoi Cell Interior Node Polygonal Domain 
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© CIMNE 2006

Authors and Affiliations

  1. 1.Department of Civil and Environmental EngineeringUniversity of CaliforniaDavisU.S.A.
  2. 2.Institute of Applied MechanicsTechnische Universität BraunschweigBraunschweigGermany

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