Development of a procedure for the solution of non-homogeneous partial differential equa- tions using the Scaled Boundary Finite Element Method

Resumo

The Scaled Boundary Finite Element Method (SBFEM) is a finite element approximation
technique in which the shape functions are constructed based on a semi-analytical approach. Due to its
features, this method is particularly efficient to approximate problems with strong internal singularities,

for instance, fracture mechanics simulation. The main focus of this study is to analyze the approxi-
mation properties of SBFEM and use them to develop a procedure to approximate non-homogeneous

partial differential equations (PDEs). It was observed optimal rates of convergence for problems with
square-root singularity. Furthermore, the orthogonality between SBFEM approximation at the boundary

and the internal bubble functions, which represent the non-homogeneous term, is observed. Such a prop-
erty is applied to extend the SBFEM to approximate non-homogeneous PDEs with internal polynomial

functions. Rates of convergence are computed to demonstrate the effectiveness of this technique.