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 . Here is the method parameter, and is the maximum spatial grid size. We further obtain the optimal error of order . 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.
Mots-clés : Alternating evolution, convection-diffusion equation, discontinuous Galerkin, error estimates, Runge-Kutta method
@article{M2AN_2018__52_5_1709_0,
author = {Liu, Hailiang and Wen, Hairui},
title = {Error estimates of the third order runge-kutta alternating evolution discontinuous galerkin method for convection-diffusion problems},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1709--1732},
publisher = {EDP-Sciences},
volume = {52},
number = {5},
year = {2018},
doi = {10.1051/m2an/2018020},
zbl = {1422.65261},
mrnumber = {3878611},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2018020/}
}
TY - JOUR AU - Liu, Hailiang AU - Wen, Hairui TI - Error estimates of the third order runge-kutta alternating evolution discontinuous galerkin method for convection-diffusion problems JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2018 SP - 1709 EP - 1732 VL - 52 IS - 5 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2018020/ DO - 10.1051/m2an/2018020 LA - en ID - M2AN_2018__52_5_1709_0 ER -
%0 Journal Article %A Liu, Hailiang %A Wen, Hairui %T Error estimates of the third order runge-kutta alternating evolution discontinuous galerkin method for convection-diffusion problems %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2018 %P 1709-1732 %V 52 %N 5 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2018020/ %R 10.1051/m2an/2018020 %G en %F M2AN_2018__52_5_1709_0
Liu, Hailiang; Wen, Hairui. Error estimates of the third order runge-kutta alternating evolution discontinuous galerkin method for convection-diffusion problems. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 52 (2018) no. 5, pp. 1709-1732. doi : 10.1051/m2an/2018020. http://www.numdam.org/articles/10.1051/m2an/2018020/
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