Global–local analysis with Element Free Galerkin Method

Meshfree methods have been used as alternatives to the Finite Element Method, due to their flexibility in building approximations without mesh alignment sensitivity. Another attractive feature is the capacity of obtaining approximate solutions of high regularity. On the other hand, the lack of the Kronecker-delta property, a more complex computation of the shape functions, and numerical integration issues represent drawbacks that can overburden the computational analysis. Aiming to conciliate the efficiency of the finite element analysis with the flexibility of meshfree methods, coupling techniques for both methods have been proposed. The coupling proposed here is based on the enrichment strategy of the Generalized Finite Element Method under the global–local approach. The global domain of the problem is represented by a coarse mesh of finite elements. A region of interest defines the local domain, discretized by a set of nodes of the Element Free Galerkin Method (EFG). This local discretization is responsible for providing a numerically obtained function used to enrich the approximate solution of the global problem. A two-dimensional numerical example is extensively evaluated to discuss the effectiveness of the approach and its behavior related to the quality of the boundary conditions of the local domain, penalty parameter, numerical integration and size of the EFG influence domain.