An \(h\)-adaptive modified element-free Galerkin method. (English) Zbl 1125.74384
Summary: In this work an \(h\)-adaptive Modified Element-Free Galerkin (MEFG) method is investigated. The proposed error estimator is based on a recovery by equilibrium of nodal patches where a recovered stress field is obtained by a moving least square approximation. The procedure generates a smooth recovered stress field that is not only more accurate then the approximate solution but also free of spurious oscillations, normally seen in EFG methods at regions with high gradient stresses or discontinuities. The MEFG method combines conventional EFG with extended partition of unity finite element (EPUFE) methods in order to create global shape functions that allow a direct imposition of the essential boundary conditions. The re-meshing of the integration mesh is based on the homogeneous error distribution criterion and upon a given prescribed admissible error. Some examples are presented, considering a plane stress assumption, which shows the performance of the proposed methodology.
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