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Implicit-Explicit Runge-Kutta schemes and finite elements with symmetric stabilization for advection-diffusion equations

Erik Burman 1, Alexandre Ern 2

(28/10/2010)

We analyze a two-stage explicit-implicit 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 $L^2$-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.

1 :	Department of Mathematics
	University of Sussex
2 :	Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique (CERMICS)
	Ecole des Ponts ParisTech

Domaine

:

Mathématiques/Analyse numérique

Mots Clés : Stabilized finite elements – Stability – Error bounds – Implicit-explicit schemes – Time-dependent PDEs

hal-00530378, version 1

http://hal.archives-ouvertes.fr/hal-00530378

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Contributeur : Alexandre Ern <>

Soumis le : Jeudi 28 Octobre 2010, 17:11:15

Dernière modification le : Jeudi 28 Octobre 2010, 17:17:11