Enriched Modified Local Green’s Function Method for singular Poisson problem

Resumo

The Modified Local Green’s Function Method (MLGFM) is a hybrid method that couples the Finite
Element Method (FEM) and the Boundary Element Method (BEM). The method presents high convergence rates
for both potential and flux in the problem boundary and does not require a priori knowledge of the fundamental
solution of the problem or a Green Function. In fact, the method automatically obtains an approximation of Green
tensor by solving an auxiliary problem. On the other hand, some improvements have been made in conventional
FEM to expand its approximation space, mainly by the Generalized Finite Element Method (GFEM) and its stable
version, the Stable Generalized Finite Element Method (SGFEM). The GFEM uses the Partition of Unity Method
idea to bring previous knowledge about the solution of the problem to enrich the traditional FEM approximation
space with appropriate functions. Here the MLGFM will be enriched with GFEM and SGFEM to obtain an
approximated Green tensor projection, using singular functions as enriched functions. This Enriched Modified
Local Green’s Function Method will be applied to singular Poisson problem and the potential and flux will be
compared with reference results.