Volume 52, Number 5, September–October 2018
|Page(s)||1709 - 1732|
|Published online||22 November 2018|
Error estimates of the third order runge-kutta alternating evolution discontinuous galerkin method for convection-diffusion problems
Iowa State University, Mathematics Department,
IA 50011, USA.
2 Beijing Institute of Technology, School of Mathematics and Statistics, Beijing 100081, P.R. China.
* Corresponding author: email@example.com
Accepted: 12 March 2018
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 + hk+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.
Mathematics Subject Classification: 65M15 / 65M60 / 35K20
Key words: Alternating evolution / convection-diffusion equation / discontinuous Galerkin / error estimates / Runge-Kutta method
© EDP Sciences, SMAI 2018
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