Journal
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
Volume 58, Issue 8, Pages 1213-1250Publisher
WILEY
DOI: 10.1002/nme.817
Keywords
least-squares; meshfree; meshless; a posteriori; error estimates; adaptive
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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 (C) 2003 John Wiley Sons, Ltd.
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