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

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posted on 2023-06-08, 12:45 authored by Erik Burman, Alexandre Ern
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 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.

History

Publication status

  • Published

File Version

  • Published version

Journal

ESAIM: Mathematical Modelling and Numerical Analysis

ISSN

0764-583X

Publisher

Société de Mathématiques Appliquées et Industrielles (SMAI)

Issue

4

Volume

46

Page range

681-707

Department affiliated with

  • Mathematics Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2012-10-22

First Open Access (FOA) Date

2012-10-22

First Compliant Deposit (FCD) Date

2012-10-22

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