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We analyze a two-stage implicit-explicit Runge-Kutta scheme for time discretization of advection-diffusion equations. Space discretization uses continuous, piecewise affine finite elements with interelement gradient jump penalty; discontinuous Galerkin methods can be considered as well. The advective and stabilization operators are treated explicitly, whereas the diffusion operator is treated implicitly. Our analysis hinges on L2-energy estimates on discrete functions in physical space. Our main results are stability and quasi-optimal error estimates for smooth solutions under a standard hyperbolic CFL restriction on the time step, both in the advection-dominated and in the diffusion-dominated regimes. The theory is illustrated by numerical examples.
@article{M2AN_2012__46_4_681_0,
author = {Burman, Erik and Ern, Alexandre},
title = {Implicit-explicit {Runge-Kutta} schemes and finite elements with symmetric stabilization for advection-diffusion equations},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {681--707},
publisher = {EDP-Sciences},
volume = {46},
number = {4},
year = {2012},
doi = {10.1051/m2an/2011047},
mrnumber = {2891466},
zbl = {1281.65123},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2011047/}
}
TY - JOUR AU - Burman, Erik AU - Ern, Alexandre TI - Implicit-explicit Runge-Kutta schemes and finite elements with symmetric stabilization for advection-diffusion equations JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2012 SP - 681 EP - 707 VL - 46 IS - 4 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/m2an/2011047/ DO - 10.1051/m2an/2011047 LA - en ID - M2AN_2012__46_4_681_0 ER -
%0 Journal Article %A Burman, Erik %A Ern, Alexandre %T Implicit-explicit Runge-Kutta schemes and finite elements with symmetric stabilization for advection-diffusion equations %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2012 %P 681-707 %V 46 %N 4 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/m2an/2011047/ %R 10.1051/m2an/2011047 %G en %F M2AN_2012__46_4_681_0
Burman, Erik; Ern, Alexandre. Implicit-explicit Runge-Kutta schemes and finite elements with symmetric stabilization for advection-diffusion equations. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 46 (2012) no. 4, pp. 681-707. doi: 10.1051/m2an/2011047
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