A SUPG formulation for solving a class of singularly perturbed steady problems in 2D

Abstract

In this presentation, approximate solutions of singularly perturbed partial differential equations are examined. It is a well-known fact that the standard Galerkin finite element method (GFEM) experiences some instability problems in obtaining accurate approximations to the solution of convection-dominated equations. Therefore, in this work, the Streamline-Upwind/Petrov-Galerkin (SUPG) method is employed to overcome the instability issues for the numerical solution of these kinds of problems. Furthermore, the stabilized scheme is supported by a shock-capturing technique. Two numerical experiments are provided to compare the results obtained by the GFEM and SUPG methods.