Implicit extended discontinuous Galerkin scheme for solving singularly perturbed Burgers' equations

Abstract

We present the implicit-modal discontinuous Galerkin scheme for solving the coupled viscous and singularly perturbed Burgers’ equations. This scheme overcomes overshoot and undershoots phenomena in the singularly perturbed Burgers’ equations. We present the stability analysis and obtain suitable ranges for penalty terms and time steps. Also, we gain the constant of trace inequality for the approximate function and its first derivatives based on Legendre basis functions. The numerical results have good agreement with the analytical and available approximate solutions.

Keywords

• discontinuous Galerkin method
• backward Euler method
• viscous Burgers’ equation
• singularly perturbed Burgers’ equation
• stability analysis