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A gradient‐based adaptation procedure and its implementation in the element‐free Galerkin method
Author(s) -
Luo Yunhua,
HäusslerCombe Ulrich
Publication year - 2003
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.615
Subject(s) - galerkin method , finite element method , adaptation (eye) , element (criminal law) , process (computing) , mathematics , strain energy density function , energy (signal processing) , computer science , algorithm , mathematical optimization , mathematical analysis , physics , structural engineering , engineering , statistics , optics , political science , law , operating system
A gradient‐based adaptation procedure is proposed in this paper. The relative error in the total strain energy from two adjacent adaptation stages is used as a stop‐criterion. The refinement–coarsening process is guided by the gradient of strain energy density, based on the assumption: a larger gradient needs a richer mesh and vice versa. The procedure is then implemented in the element‐free Galerkin method for linear elasto‐static problems. Numerical examples are presented to show the performance of the proposed procedure. Copyright © 2003 John Wiley & Sons, Ltd.