Element-free Galerkin methods in combination with finite element approaches Original Research Article

Element Free Galerkin (EFG) methods are methods for solving partial differential equations with the help of shape functions coming from Moving Least Squares Approximation. The EFG-method is more flexible than the Finite Element (FE) method, since it requires only nodal data and no element connectivity is needed. Because the EFG-method is computationally expensive, combinations of the EFG-method and the FE-method are considered. Implementations based on several weak forms of the problem description are studied. Numerical examples in elastostatics and fracture mechanics show that the implementations are able to compute both displacement and stress fields accurately.