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

ESAIM: Mathematical Modelling and Numerical Analysis (2012)

- Volume: 46, Issue: 4, page 681-707
- ISSN: 0764-583X

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topBurman, Erik, and Ern, Alexandre. "Implicit-explicit Runge–Kutta schemes and finite elements with symmetric stabilization for advection-diffusion equations." ESAIM: Mathematical Modelling and Numerical Analysis 46.4 (2012): 681-707. <http://eudml.org/doc/277842>.

@article{Burman2012,

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 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.},

author = {Burman, Erik, Ern, Alexandre},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Stabilized finite elements; stability; error bounds; implicit-explicit Runge–Kutta schemes; unsteady convection-diffusion; stabilized finite elements; implicit-explicit Runge-Kutta schemes; semidiscretization; advection-diffusion equations; smooth solution; convergence; numerical experiment},

language = {eng},

month = {2},

number = {4},

pages = {681-707},

publisher = {EDP Sciences},

title = {Implicit-explicit Runge–Kutta schemes and finite elements with symmetric stabilization for advection-diffusion equations},

url = {http://eudml.org/doc/277842},

volume = {46},

year = {2012},

}

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

DA - 2012/2//

PB - EDP Sciences

VL - 46

IS - 4

SP - 681

EP - 707

AB - 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.

LA - eng

KW - Stabilized finite elements; stability; error bounds; implicit-explicit Runge–Kutta schemes; unsteady convection-diffusion; stabilized finite elements; implicit-explicit Runge-Kutta schemes; semidiscretization; advection-diffusion equations; smooth solution; convergence; numerical experiment

UR - http://eudml.org/doc/277842

ER -

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