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Moving particle finite element method with global smoothness. (English) Zbl 1065.74608
Summary: We describe a new version of the moving particle finite element method (MPFEM) that provides solutions within a $$C^0$$ finite element framework. The finite elements determine the weighting for the moving partition of unity. A concept of General Shape Function is proposed which extends regular finite element shape functions to a larger domain. These are combined with Shepard functions to obtain a smooth approximation. The Moving Particle Finite Element Method combines desirable features of finite element and meshfree methods. The proposed approach, in fact, can be interpreted as a moving partition of unity finite element method or moving kernel finite element method. This method possesses the robustness and efficiency of the $$C^0$$ finite element method while providing at least $$C^1$$ continuity.

##### MSC:
 74S05 Finite element methods applied to problems in solid mechanics 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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