Implicit-Explicit Runge-Kutta schemes and finite elements with symmetric stabilization for advection-diffusion equations - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2010

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

Résumé

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.
Fichier principal
Vignette du fichier
imex.pdf (459.99 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00530378 , version 1 (28-10-2010)

Identifiants

  • HAL Id : hal-00530378 , version 1

Citer

Erik Burman, Alexandre Ern. Implicit-Explicit Runge-Kutta schemes and finite elements with symmetric stabilization for advection-diffusion equations. 2010. ⟨hal-00530378⟩
150 Consultations
569 Téléchargements

Partager

Gmail Facebook X LinkedIn More