scholarly journals On the stability of conservative discontinuous Galerkin/Hermite Spectral methods for the Vlasov-Poisson System

2021 ◽  
pp. 110881
Author(s):  
Marianne Bessemoulin-Chatard ◽  
Francis Filbet
Keyword(s):  
Discontinuous Galerkin ◽  
Spectral Methods ◽  
Poisson System ◽  
The Stability ◽  
Hermite Spectral Methods

The stability of stationary solution for outflow problem on the navier-stokes-poisson system

2016 ◽  
Vol 36 (4) ◽  
pp. 1098-1116 ◽  
Author(s):  
Mina JIANG ◽  
Suhua LAI ◽  
Haiyan YIN ◽  
Changjiang ZHU
Keyword(s):  
Stationary Solution ◽  
Navier Stokes ◽  
Poisson System ◽  
The Stability

A STUDY OF HIGHER-ORDER DISCONTINUOUS GALERKIN AND QUADRATIC LEAST-SQUARES STABILIZED FINITE ELEMENT COMPUTATIONS FOR ACOUSTICS

2006 ◽  
Vol 14 (01) ◽  
pp. 1-19 ◽  
Author(s):  
ISAAC HARARI ◽  
RADEK TEZAUR ◽  
CHARBEL FARHAT
Keyword(s):  
Least Squares ◽  
Discontinuous Galerkin ◽  
Large Scale ◽  
Dispersion Analysis ◽  
Stability Parameter ◽  
New Approach ◽  
One Dimensional ◽  
Stabilized Finite Element ◽  
Quadratic Interpolation ◽  
The Stability

One-dimensional analyses provide novel definitions of the Galerkin/least-squares stability parameter for quadratic interpolation. A new approach to the dispersion analysis of the Lagrange multiplier approximation in discontinuous Galerkin methods is presented. A series of computations comparing the performance of [Formula: see text] Galerkin and GLS methods with Q-8-2 DGM on large-scale problems shows superior DGM results on analogous meshes, both structured and unstructured. The degradation of the [Formula: see text] GLS stabilization on unstructured meshes may be a consequence of inadequate one-dimensional analysis used to derive the stability parameter.

scholarly journals Numerical Simulation of Microflows Using Hermite Spectral Methods

2020 ◽  
Vol 42 (1) ◽  
pp. B105-B134 ◽  
Author(s):  
Zhicheng Hu ◽  
Zhenning Cai ◽  
Yanli Wang
Keyword(s):  
Numerical Simulation ◽  
Spectral Methods ◽  
Hermite Spectral Methods

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.

scholarly journals Stability of disk-like galaxies – Part I: Stability via reduction

Analysis ◽  
2006 ◽  
Vol 26 (4) ◽  
Author(s):  
Roman Fiřt ◽  
Gerhard Rein
Keyword(s):  
Stability Problem ◽  
Variational Approach ◽  
Steady States ◽  
Poisson System ◽  
Reduction Procedure ◽  
Analogous Question ◽  
Existence And Stability ◽  
The Stability

We prove the existence and stability of flat steady states of the Vlasov–Poisson system, which in astrophysics are used as models of disk-like galaxies. We follow the variational approach developed by GUO and REIN [5, 6, 7] for this type of problems and extend previous results of REIN [11]. In particular, we employ a reduction procedure which relates the stability problem for the Vlasov–Poisson system to the analogous question for the Euler–Poisson system.

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