Adaptive methodology for meshless finite point method

Authors:
F. Perazzo;R. Löhner;L. Perez-Pozo
Affiliations:
Department of Mechanical Engineering, Universidad Técnica Federico Santa María, Avenida España 1680, Valparaíso, Chile;School of Computational Science and Informatics, George Mason University, M.S. 4C7, Fairfax, VA 22030-4444, USA;Department of Mechanical Engineering, Universidad Técnica Federico Santa María, Avenida España 1680, Valparaíso, Chile
Venue:
Advances in Engineering Software
Year:
2008

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Abstract

In this work, a posteriori error estimator and an adaptive refinement process for the meshless finite point method (FPM), which is based on point collocation, are presented. The error indicator is formulated by the least-squares functional evaluation, used in the shape function development. New degrees of freedom or additional points can be incorporated without difficulty, in zones where the error estimator presents a high value, by means of h-p refinement processes. The validity of the proposed error estimator can be demonstrated by developments of numerical problems in mechanics of solids, using an adaptive refinement process of the solution.