Adaptive analysis using the node-based smoothed finite element method (NS-FEM).

*(English)*Zbl 1370.74144Summary: The paper presents an adaptive analysis within the framework of the node-based smoothed finite element method (NS-FEM) using triangular elements. An error indicator based on the recovery strain is used and shown to be asymptotically exact by an effectivity index and numerical results. A simple refinement strategy using the newest node bisection is briefly presented. The numerical results of some benchmark problems show that the present adaptive procedure can accurately catch the appearance of the steep gradient of stresses and the occurrence of refinement is concentrated properly. The energy error norms of adaptive models for both NS-FEM and FEM obtain higher convergence rate compared with the uniformly refined models, but the results of NS-FEM are better and achieve higher convergence rate than those of FEM. The effectivity index of NS-FEM is also closer and approaches to unity faster than that of FEM. The upper bound property in the strain energy of NS-FEM is always verified during the adaptive procedure.

##### 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 |

65N50 | Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs |

##### Keywords:

finite element method (FEM); meshfree methods; node-based smoothed finite element method (NS-FEM); upper bound; error indicator; adaptive analysis
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\textit{T. Nguyen-Thoi} et al., Int. J. Numer. Methods Biomed. Eng. 27, No. 2, 198--218 (2011; Zbl 1370.74144)

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