# A new approach for the Modified Local Green’s Function Method applied to Poisson equation

## Palavras-chave:

Green Functions, Modified Local Green’s Function Method, Finite Element Method, Boundary Ele- ment Method## Resumo

Originally proposed at the end of the 80 ’s, the Modified Local Green’s Function Method (MLGFM) is

an integral method that was described as a hybrid of the Finite Element Method (FEM) and the Boundary Element

Method (BEM). The method was proposed to apply the BEM methodology to problems with no knowledge of

the fundamental solution. Essentially, the MLGFM creates discrete projections of the Green’s function solving

an auxiliary domain problem, and this problem can be solved, for example, by the FEM formulation. Despite the

good convergence of the secondary variable in the boundary, the method has a major disadvantage over FEM, the

obtainment of the Green’s function projections implies in to solve the system of equations in the domain, resulting

in a great computational effort. However, this paper aims to show a new approach to the MLGFM where it is

not necessary to obtain the Green’s projections and the final equations system has the same number of degrees

of freedom as FEM and still presents high convergence for the secondary variable in the boundary. The new

formulation can be obtained directly by the weighted residual sentence and variables using the same approximation

of the original MLGFM. The processing time of the two approaches are compared and the method is applied to

Poisson Equation.