scholarly journals NUMERICAL SIMULATION OF A SINGLE RING INFILTRATION EXPERIMENT WITH hp-ADAPTIVE SPACE-TIME DISCONTINUOUS GALERKIN METHOD

2021 ◽  
Vol 61 (SI) ◽  
pp. 59-67
Author(s):  
Vít Dolejší ◽  
Michal Kuráž ◽  
Pavel Solin
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Space Time ◽  
Time Dependent ◽  
Richards Equation ◽  
Fine Mesh ◽  
Single Ring ◽  
Seepage Face ◽  
Infiltration Experiment

We present a novel hp-adaptive space-time discontinuous Galerkin (hp-STDG) method for the numerical solution of the nonstationary Richards equation equipped with Dirichlet, Neumann and seepage face boundary conditions. The hp-STDG method presented in this paper is a generalization of a hp-STDG method which was developed for time dependent non-linear convective-diffusive problems. We describe the method and the single ring experiment, and then we present a numerical experiment which clearly demonstrates the superiority of the hp-STDG method over a discontinuous Galerkin method based on a static fine mesh.

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.

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
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