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

Burman, Erik and Ern, Alexandre (2012) Implicit-explicit Runge–Kutta schemes and finite elements with symmetric stabilization for advection-diffusion equations. ESAIM: Mathematical Modelling and Numerical Analysis, 46 (4). pp. 681-707. ISSN 0764-583X

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Abstract

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.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics
Related URLs:
Depositing User: Catrina Hey
Date Deposited: 22 Oct 2012 15:35
Last Modified: 14 Mar 2017 02:09
URI: http://sro.sussex.ac.uk/id/eprint/41415

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