A SUPG stabilized scaled boundary finite element method for convection-diffusion problems

In this paper, we extend the scaled boundary finite element method (SBFEM) to steady state convection–diffusion problems with stabilization based on Streamline–Upwind Petrov–Galerkin (SUPG). The SBFEM offers a semi-analytical framework, naturally accommodates elements with hanging nodes and does not impose restrictions on the shape and quality of the elements used for spatial discretization, thus relaxing the meshing burden. On the other hand, SUPG ensures stability of the solution whilst preserving accuracy and suppresses numerical instabilities. The potential of combining the computational efficiency and geometry flexibility offered by the SBFEM with the robustness of the SUPG stabilization is demonstrated through a series of numerical examples of varying complexities. From the systematic numerical study, it is inferred that the proposed framework exhibits improved performance and the results converge at optimal convergence rate.