Theory of the Space-Time Discontinuous Galerkin Method for Nonstationary Parabolic Problems with Nonlinear Convection and Diffusion

2012 ◽  
Vol 50 (3) ◽  
pp. 1181-1206 ◽  
Author(s):  
Jan Česenek ◽  
Miloslav Feistauer
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Space Time ◽  
Parabolic Problems ◽  
Nonlinear Convection ◽  
And Diffusion

scholarly journals A splitting mixed space-time discontinuous Galerkin method for parabolic problems

2012 ◽  
Vol 31 ◽  
pp. 1050-1059 ◽  
Author(s):  
Siriguleng He ◽  
Hong Li ◽  
Yang Liu ◽  
Zhichao Fang ◽  
Jingbo Yang ◽  
...  
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Space Time ◽  
Parabolic Problems

scholarly journals Stability of the ale space-time discontinuous Galerkin method for nonlinear convection-diffusion problems in time-dependent domains

2018 ◽  
Vol 52 (6) ◽  
pp. 2327-2356
Author(s):  
Monika Balázsová ◽  
Miloslav Feistauer ◽  
Miloslav Vlasák
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Time Derivative ◽  
Space Time ◽  
Time Dependent ◽  
Nonlinear Convection ◽  
Convection Diffusion ◽  
Time Dependent Domain ◽  
Ale Space

The paper is concerned with the analysis of the space-time discontinuous Galerkin method (STDGM) applied to the numerical solution of nonstationary nonlinear convection-diffusion initial- boundary value problem in a time-dependent domain. The problem is reformulated using the arbitrary Lagrangian-Eulerian (ALE) method, which replaces the classical partial time derivative by the so-called ALE derivative and an additional convective term. The problem is discretized with the use of the ALE- space time discontinuous Galerkin method (ALE-STDGM). 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 main attention is paid to the proof of the unconditional stability of the method. An important step is the generalization of a discrete characteristic function associated with the approximate solution and the derivation of its properties.

On the stability of the space–time discontinuous Galerkin method for the numerical solution of nonstationary nonlinear convection–diffusion problems

2015 ◽  
Vol 23 (3) ◽  
Author(s):  
Monika Balázsová ◽  
Miloslav Feistauer ◽  
Martin Hadrava ◽  
Adam Kosík
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Space Time ◽  
Nonlinear Convection ◽  
Convection Diffusion ◽  
The Subject ◽  
The Stability ◽  
Theoretical Results ◽  
Diffusion Problems

AbstractThe subject of this paper is the analysis of the space-time discontinuous Galerkin method for the solution of nonstationary, nonlinear, convection-diffusion problems. In the formulation of the numerical scheme, the nonsymmetric, symmetric and incomplete versions of the discretization of diffusion terms and interior and boundary penalty are used. Then error estimates are briefly characterized. The main attention is paid to the investigation of unconditional stability of the method. An important tool is the concept of the discrete characteristic function. Theoretical results are accompanied by numerical experiments.

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