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A posteriori error estimates and an adaptive scheme of least‐squares meshfree method
Author(s) -
Park SangHoon,
Kwon KieChan,
Youn SungKie
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.817
Subject(s) - a priori and a posteriori , residual , voronoi diagram , mathematics , adaptive mesh refinement , moving least squares , scheme (mathematics) , least squares function approximation , algorithm , mathematical optimization , computer science , geometry , mathematical analysis , statistics , computational science , philosophy , epistemology , estimator
A posteriori error estimates and an adaptive refinement scheme of first‐order least‐squares meshfree method (LSMFM) are presented. The error indicators are readily computed from the residual. For an elliptic problem, the error indicators are further improved by applying the Aubin–Nitsche method. It is demonstrated, through numerical examples, that the error indicators coherently reflect the actual error. In the proposed refinement scheme, Voronoi cells are used for inserting new nodes at appropriate positions. Numerical examples show that the adaptive first‐order LSMFM, which combines the proposed error indicators and nodal refinement scheme, is effectively applied to the localized problems such as the shock formation in fluid dynamics. Copyright © 2003 John Wiley & Sons, Ltd.