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Zbl 1145.74041
Rabczuk, T.; Belytschko, T.
Adaptivity for structured meshfree particle methods in 2D and 3D. (English)
[J] Int. J. Numer. Methods Eng. 63, No. 11, 1559-1582 (2005). ISSN 0029-5981

Summary: We describe the implementation of $h$-adaptivity for meshfree particle methods within a structured framework. In this framework, the initial particle arrangement is structured along with a background mesh, and outside boundaries and interior interfaces are described by implicit functions. The advantage of meshfree approximations in this framework lies in the ease of implementing $h$-adaptivity and the simplicity of data structures. Particles can easily be added and removed without complications in the data structure, although there are some issues in the quadrature. An a posteriori error estimation is used for the adaptive refinement. An adaptive refinement strategy is applied to several linear elastic problems with high stress and strain gradients and singularities. Several nonlinear examples are also given.

MSC 2000:: *74S30 Other numerical methods

Keywords: error estimation; level sets; high gradients

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Zentralblatt MATH Berlin [Germany]