Convergence analysis of the scaled boundary finite element method for the Laplace equation

Abstract The scaled boundary finite element method (SBFEM) is a relatively recent that allows the approximation of solutions to partial differential equations (PDEs) without need fundamental solution. A theoretical framework for convergence analysis SBFEM proposed here. This achieved by defining space semi-discrete functions and constructing an interpolation operator onto this space. We prove error estimates show optimal solution can be obtained in SBFEM. These results are backed two numerical examples.