Error estimates of the third order runge-kutta alternating evolution discontinuous galerkin method for convection-diffusion problems

¹ Iowa State University, Mathematics Department, Ames, IA 50011, USA.
² Beijing Institute of Technology, School of Mathematics and Statistics, Beijing 100081, P.R. China.

^* Corresponding author: wenhr@bit.edu.cn

Received: 13 September 2017
Accepted: 12 March 2018

Abstract

In this paper, we present the stability analysis and error estimates for the alternating evolution discontinuous Galerkin (AEDG) method with third order explicit Runge-Kutta temporal discretization for linear convection-diffusion equations. The scheme is shown stable under a CFL-like stability condition c₀τ ≤ ε ≤ c₁h². Here ε is the method parameter, and h is the maximum spatial grid size. We further obtain the optimal L² error of order O(τ³ + h^k+1). Key tools include two approximation finite element spaces to distinguish overlapping polynomials, coupled global projections, and energy estimates of errors. For completeness, the stability analysis and error estimates for second order explicit Runge-Kutta temporal discretization is included in the appendix.