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Conforming polygonal finite elements
Author(s) -
Sukumar N.,
Tabarraei A.
Publication year - 2004
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1141
Subject(s) - polygon (computer graphics) , finite element method , polygon mesh , regular polygon , mathematics , mesh generation , basis function , geometry , computer science , mathematical analysis , structural engineering , frame (networking) , telecommunications , engineering
In this paper, conforming finite elements on polygon meshes are developed. Polygonal finite elements provide greater flexibility in mesh generation and are better‐suited for applications in solid mechanics which involve a significant change in the topology of the material domain. In this study, recent advances in meshfree approximations, computational geometry, and computer graphics are used to construct different trial and test approximations on polygonal elements. A particular and notable contribution is the use of meshfree (natural‐neighbour, nn) basis functions on a canonical element combined with an affine map to construct conforming approximations on convex polygons. This numerical formulation enables the construction of conforming approximation on n ‐gons ( n ⩾3), and hence extends the potential applications of finite elements to convex polygons of arbitrary order. Numerical experiments on second‐order elliptic boundary‐value problems are presented to demonstrate the accuracy and convergence of the proposed method. Copyright © 2004 John Wiley & Sons, Ltd.