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C 1 macroelements in adaptive finite element methods
Author(s) -
Stogner Roy H.,
Carey Graham F.
Publication year - 2006
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.1912
Subject(s) - a priori and a posteriori , convergence (economics) , tetrahedron , polygon mesh , mathematics , finite element method , function (biology) , algorithm , rate of convergence , computer science , geometry , structural engineering , engineering , key (lock) , philosophy , computer security , epistemology , evolutionary biology , economics , biology , economic growth
Some interesting properties of composite basis functions for C 1 macroelements are investigated, including their use for constructing conforming C 1 function spaces on non‐conforming adaptively refined meshes. Of particular interest is the classical cubic Hsieh–Clough–Tocher 3‐split triangle because of its simplicity and convergence properties in fourth‐order problems, as compared with the Powell–Sabin–Heindl 6‐split and 12‐split triangles. A posteriori error indicators for adaptive refinement are developed. Numerical experiments demonstrate convergence rates, and adaptive refinement performance based on a simplified error indicator is tested. Extensibility to analogous three‐dimensional tetrahedral elements is briefly discussed. Copyright © 2006 John Wiley & Sons, Ltd.