Stability of Nonlinear Convection-Diffusion-Reaction Systems in Discontinuous Galerkin Methods

被引：10

作者：

Michoski, C. ^{[1
,2
]}

Alexanderian, A. ^{[2
,3
]}

Paillet, C. ^{[5
]}

Kubatko, E. J. ^{[4
]}

Dawson, C. ^{[2
]}

机构：

[1] Univ Colorado, Computat Mech & Geometry Lab CMGLab, Aerosp Engn Sci, Boulder, CO 80302 USA

[2] Univ Texas Austin, ICES, Austin, TX 78712 USA

[3] North Carolina State Univ, Dept Math, Raleigh, NC 27695 USA

[4] Ohio State Univ, Civil Engn & Geodet Engn Dept, Columbus, OH 43210 USA

[5] Ecole Normale Super, Dept Mech Engn, F-94230 Cachan, France

来源：

JOURNAL OF SCIENTIFIC COMPUTING | 2017年 / 70卷 / 02期

基金：

美国国家科学基金会;

关键词：

Stability analysis; Nonlinear; von Neumann; Discontinuous Galerkin; Runge-Kutta methods; RKSSP; RKC; Convection-Reaction-Diffusion; OPERATOR SPLITTING METHODS; RUNGE-KUTTA METHODS; INDEFINITE OPERATORS; EXPLICIT; ORDER; EQUATIONS;

D O I：

10.1007/s10915-016-0256-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this work we provide an extension of the classical von Neumann stability analysis for high-order accurate discontinuous Galerkin methods applied to generalized nonlinear convection-reaction-diffusion systems. We provide a partial linearization under which a sufficient condition emerges that guarantees stability in this context. The stability behavior of these systems is then closely analyzed relative to Runge-Kutta Chebyshev (RKC) and strong stability preserving (RKSSP) temporal discretizations over a nonlinear system of reactive compressible gases arising in the study of atmospheric chemistry.

引用

页码：516 / 550

页数：35

共 50 条

[41] Application of Discontinuous Galerkin Methods for Reaction-Diffusion Systems in Developmental Biology
Zhu, Jianfeng
Zhang, Yong-Tao
Newman, Stuart A.
Alber, Mark
JOURNAL OF SCIENTIFIC COMPUTING, 2009, 40 (1-3) : 391 - 418
[42] Adaptive discontinuous Galerkin methods for non-linear diffusion-convection-reaction equations
Uzunca, Murat
Karasozen, Bulent
Manguoglu, Murat
COMPUTERS & CHEMICAL ENGINEERING, 2014, 68 : 24 - 37
[43] Stability estimates in identification problems for the convection-diffusion-reaction equation
G. V. Alekseev
I. S. Vakhitov
O. V. Soboleva
Computational Mathematics and Mathematical Physics, 2012, 52 : 1635 - 1649
[44] Variational multiscale element free Galerkin method for convection-diffusion-reaction equation with small diffusion
Zhang, Xiaohua
Xiang, Hui
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, 2014, 46 : 85 - 92
[45] On the Stability of Continuous-Discontinuous Galerkin Methods for Advection-Diffusion-Reaction Problems
Cangiani, Andrea
Chapman, John
Georgoulis, Emmanuil
Jensen, Max
JOURNAL OF SCIENTIFIC COMPUTING, 2013, 57 (02) : 313 - 330
[46] Adaptive Iterative Splitting Methods for Convection-Diffusion-Reaction Equations
Geiser, Juergen
Hueso, Jose L.
Martinez, Eulalia
MATHEMATICS, 2020, 8 (03)
[47] GALERKIN AND LEAST SQUARES METHODS TO SOLVE A 3D CONVECTION-DIFFUSION-REACTION EQUATION WITH VARIABLE COEFFICIENTS
Romao, Estaner Claro
Mendes de Moura, Luiz Felipe
NUMERICAL HEAT TRANSFER PART A-APPLICATIONS, 2012, 61 (09) : 669 - 698
[48] Numerical Methods for the Time Fractional Convection-Diffusion-Reaction Equation
Li, Changpin
Wang, Zhen
NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2021, 42 (10) : 1115 - 1153
[49] A finite volume discontinuous Galerkin scheme¶for nonlinear convection–diffusion problems
V. Dolejší
M. Feistauer
C. Schwab
CALCOLO, 2002, 39 : 1 - 40
[50] Analysis of the discontinuous Galerkin method for nonlinear convection-diffusion problems
Dolejsí, V
Feistauer, M
Sobotíková, V
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2005, 194 (25-26) : 2709 - 2733

← 1 2 3 4 5 →