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Zbl 0796.73077
Belytschko, T.; Lu, Y.Y.; Gu, L.
Element-free Galerkin methods. (English)
[J] Int. J. Numer. Methods Eng. 37, No.2, 229-256 (1994). ISSN 0029-5981

An element-free Galerkin method which is applicable to arbitrary shapes but requires only nodal data is applied to elasticity and heat conduction problems. In this method, moving least-squares interpolants are used to construct the trial and test functions for the variational principle (weak form); the dependent variable and its gradient are continuous in the entire domain. The numerical examples show that with these modifications, the method does not exhibit any volumetric locking, the rate of convergence can exceed that of finite elements significantly and a high resolution of localized steep gradients can be achieved. The moving least-squares interpolants and the choices of the weight function are also discussed.

MSC 2000:: *74S30 Other numerical methods
74P10 Optimization of other properties
74S05 Finite element methods
74B99 Elasitc materials
80A20 Heat and mass transfer

Keywords: moving least-squares interpolants; variational principle; convergence; resolution of localized steep gradients; weight function

Cited in: Zbl 1157.74050 Zbl 0869.65069

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