scholarly journals Discontinuous Galerkin methods for the one-dimensional Vlasov-Poisson system

2011 ◽  
Vol 4 (4) ◽  
pp. 955-989 ◽  
Author(s):  
Blanca Ayuso ◽  
◽  
José A. Carrillo ◽  
Chi-Wang Shu ◽  
◽  
...  
Keyword(s):  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Methods ◽  
Galerkin Methods ◽  
Poisson System ◽  
One Dimensional ◽  
The One

scholarly journals DISCONTINUOUS GALERKIN METHODS FOR THE MULTI-DIMENSIONAL VLASOV–POISSON PROBLEM

2012 ◽  
Vol 22 (12) ◽  
pp. 1250042 ◽  
Author(s):  
BLANCA AYUSO DE DIOS ◽  
JOSÉ A. CARRILLO ◽  
CHI-WANG SHU
Keyword(s):  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Methods ◽  
Mixed Finite Element ◽  
Galerkin Approximation ◽  
Mixed Finite Element Method ◽  
Optimal Error Estimates ◽  
Galerkin Methods ◽  
Poisson System ◽  
Optimal Error ◽  
Poisson Problem

We introduce and analyze two new semi-discrete numerical methods for the multi-dimensional Vlasov–Poisson system. The schemes are constructed by combining a discontinuous Galerkin approximation to the Vlasov equation together with a mixed finite element method for the Poisson problem. We show optimal error estimates in the case of smooth compactly supported initial data. We propose a scheme that preserves the total energy of the system.

$L^2$ stable discontinuous Galerkin methods for one-dimensional two-way wave equations

2016 ◽  
Vol 86 (303) ◽  
pp. 121-155 ◽  
Author(s):  
Yingda Cheng ◽  
Ching-Shan Chou ◽  
Fengyan Li ◽  
Yulong Xing
Keyword(s):  
Discontinuous Galerkin ◽  
Wave Equations ◽  
Discontinuous Galerkin Methods ◽  
Galerkin Methods ◽  
One Dimensional
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