High-Order Shape Functions in the Scaled Boundary Finite Element Method Revisited

The scaled boundary finite element method (SBFEM) is a semi-analytical approach to solving partial differential equations, in which a finite element approximation is deployed for the domain's boundary, while analytical solutions are sought to describe the behavior in the interior of the domain. Since the inception of SBFEM, a number of different shape functions have been applied to interpolate the solution on the boundary. The overarching goal of this communication is to review the respective advantages and disadvantages of the available interpolants in the context of the SBFEM and develop recommendations regarding their application. In addition, we discuss in detail the discretization employed in the so-called diagonal SBFEM.

Automated summary

The scaled boundary finite element method (SBFEM) is a semi-analytical approach that combines finite element approximation with analytical solutions to solve partial differential equations. Various shape functions have been used to interpolate solutions on the boundary. This study aims to review the advantages and disadvantages of different interpolants in the context of SBFEM and provide recommendations for their application.