On the stability of the ALE space-time discontinuous Galerkin method for nonlinear convection-diffusion problems in time-dependent domains

Martin Balazovjech; Miloslav Feistauer

Applications of Mathematics (2015)

  • Volume: 60, Issue: 5, page 501-526
  • ISSN: 0862-7940

Abstract

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The paper is concerned with the analysis of the space-time discontinuous Galerkin method (STDGM) applied to the numerical solution of the nonstationary nonlinear convection-diffusion initial-boundary value problem in a time-dependent domain formulated with the aid of the arbitrary Lagrangian-Eulerian (ALE) method. In the formulation of the numerical scheme we use the nonsymmetric, symmetric and incomplete versions of the space discretization of diffusion terms and interior and boundary penalty. The nonlinear convection terms are discretized with the aid of a numerical flux. The space discretization uses piecewise polynomial approximations of degree not greater than p with an integer p ≥ 1 . In the theoretical analysis, the piecewise linear time discretization is used. The main attention is paid to the investigation of unconditional stability of the method.

How to cite

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Balazovjech, Martin, and Feistauer, Miloslav. "On the stability of the ALE space-time discontinuous Galerkin method for nonlinear convection-diffusion problems in time-dependent domains." Applications of Mathematics 60.5 (2015): 501-526. <http://eudml.org/doc/271601>.

@article{Balazovjech2015,
abstract = {The paper is concerned with the analysis of the space-time discontinuous Galerkin method (STDGM) applied to the numerical solution of the nonstationary nonlinear convection-diffusion initial-boundary value problem in a time-dependent domain formulated with the aid of the arbitrary Lagrangian-Eulerian (ALE) method. In the formulation of the numerical scheme we use the nonsymmetric, symmetric and incomplete versions of the space discretization of diffusion terms and interior and boundary penalty. The nonlinear convection terms are discretized with the aid of a numerical flux. The space discretization uses piecewise polynomial approximations of degree not greater than $p$ with an integer $p\ge 1$. In the theoretical analysis, the piecewise linear time discretization is used. The main attention is paid to the investigation of unconditional stability of the method.},
author = {Balazovjech, Martin, Feistauer, Miloslav},
journal = {Applications of Mathematics},
keywords = {nonstationary nonlinear convection-diffusion equations; time-dependent domain; ALE method; space-time discontinuous Galerkin method; unconditional stability; nonstationary nonlinear convection-diffusion equations; time-dependent domain; ALE method; space-time discontinuous Galerkin method; unconditional stability},
language = {eng},
number = {5},
pages = {501-526},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the stability of the ALE space-time discontinuous Galerkin method for nonlinear convection-diffusion problems in time-dependent domains},
url = {http://eudml.org/doc/271601},
volume = {60},
year = {2015},
}

TY - JOUR
AU - Balazovjech, Martin
AU - Feistauer, Miloslav
TI - On the stability of the ALE space-time discontinuous Galerkin method for nonlinear convection-diffusion problems in time-dependent domains
JO - Applications of Mathematics
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 60
IS - 5
SP - 501
EP - 526
AB - The paper is concerned with the analysis of the space-time discontinuous Galerkin method (STDGM) applied to the numerical solution of the nonstationary nonlinear convection-diffusion initial-boundary value problem in a time-dependent domain formulated with the aid of the arbitrary Lagrangian-Eulerian (ALE) method. In the formulation of the numerical scheme we use the nonsymmetric, symmetric and incomplete versions of the space discretization of diffusion terms and interior and boundary penalty. The nonlinear convection terms are discretized with the aid of a numerical flux. The space discretization uses piecewise polynomial approximations of degree not greater than $p$ with an integer $p\ge 1$. In the theoretical analysis, the piecewise linear time discretization is used. The main attention is paid to the investigation of unconditional stability of the method.
LA - eng
KW - nonstationary nonlinear convection-diffusion equations; time-dependent domain; ALE method; space-time discontinuous Galerkin method; unconditional stability; nonstationary nonlinear convection-diffusion equations; time-dependent domain; ALE method; space-time discontinuous Galerkin method; unconditional stability
UR - http://eudml.org/doc/271601
ER -

References

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