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A p ‐hierarchical adaptive procedure for the scaled boundary finite element method
Author(s) -
Vu Thu Hang,
Deeks Andrew J.
Publication year - 2007
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.2055
Subject(s) - estimator , finite element method , norm (philosophy) , bounded function , mathematics , mathematical optimization , domain (mathematical analysis) , boundary (topology) , computer science , algorithm , mathematical analysis , statistics , physics , political science , law , thermodynamics
This paper describes a p ‐hierarchical adaptive procedure based on minimizing the classical energy norm for the scaled boundary finite element method. The reference solution , which is the solution of the fine mesh formed by uniformly refining the current mesh element‐wise one order higher, is used to represent the unknown exact solution. The optimum mesh is assumed to be obtained when each element contributes equally to the global error. The refinement criteria and the energy norm‐based error estimator are described and formulated for the scaled boundary finite element method. The effectivity index is derived and used to examine quality of the proposed error estimator. An algorithm for implementing the proposed p ‐hierarchical adaptive procedure is developed. Numerical studies are performed on various bounded domain and unbounded domain problems. The results reflect a number of key points. Higher‐order elements are shown to be highly efficient. The effectivity index indicates that the proposed error estimator based on the classical energy norm works effectively and that the reference solution employed is a high‐quality approximation of the exact solution. The proposed p ‐hierarchical adaptive strategy works efficiently. Copyright © 2007 John Wiley & Sons, Ltd.