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

被引：0
|
作者：
C. Michoski
A. Alexanderian
C. Paillet
E. J. Kubatko
C. Dawson
机构：
[1] University of Colorado at Boulder,Aerospace Engineering Sciences, Computational Mechanics and Geometry Laboratory (CMGLab)
[2] University of Texas at Austin,Institute for Computational Engineering and Sciences (ICES)
[3] North Carolina State University,Department of Mathematics
[4] The Ohio State University,Civil Engineering and Geodetic Engineering Department
[5] École normale supérieure de Cachan,Department of Mechanical Engineering
来源：
Journal of Scientific Computing | 2017年 / 70卷
关键词：
Stability analysis; Nonlinear; von Neumann; Discontinuous Galerkin; Runge–Kutta methods; RKSSP; RKC; Convection–Reaction–Diffusion;
D O I：
暂无
中图分类号：
学科分类号：
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
收藏
页码：516 / 550
页数：34
相关论文
共 50 条
  • [1] Stability of Nonlinear Convection-Diffusion-Reaction Systems in Discontinuous Galerkin Methods
    Michoski, C.
    Alexanderian, A.
    Paillet, C.
    Kubatko, E. J.
    Dawson, C.
    [J]. JOURNAL OF SCIENTIFIC COMPUTING, 2017, 70 (02) : 516 - 550
  • [2] Adaptive discontinuous galerkin methods for nonlinear diffusion-convection-reaction equations
    Karasözen, Bulent
    Uzunca, Murat
    Manguoğlu, Murat
    [J]. Lecture Notes in Computational Science and Engineering, 2015, 103 : 85 - 93
  • [3] Adaptive discontinuous galerkin methods for nonlinear diffusion-convection-reaction equations
    Karasözen, Bulent
    Uzunca, Murat
    Manguoǧlu, Murat
    [J]. Lecture Notes in Computational Science and Engineering, 2015, 103 : 85 - 93
  • [4] SPACETIME DISCONTINUOUS GALERKIN METHODS FOR SOLVING CONVECTION-DIFFUSION SYSTEMS
    May, Sandra
    [J]. ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2017, 51 (05): : 1755 - 1781
  • [5] On the Stability of Continuous–Discontinuous Galerkin Methods for Advection–Diffusion–Reaction Problems
    Andrea Cangiani
    John Chapman
    Emmanuil Georgoulis
    Max Jensen
    [J]. Journal of Scientific Computing, 2013, 57 : 313 - 330
  • [6] Discontinuous Galerkin Method Based on the Reduced Space for the Nonlinear Convection–Diffusion–Reaction Equation
    Shijin Hou
    Yinhua Xia
    [J]. Journal of Scientific Computing, 2024, 99
  • [7] Using Krylov-subspace iterations in discontinuous Galerkin methods for nonlinear reaction-diffusion systems
    Estep, DJ
    Freund, RW
    [J]. DISCONTINUOUS GALERKIN METHODS: THEORY, COMPUTATION AND APPLICATIONS, 2000, 11 : 327 - 335
  • [8] Superconvergence of Discontinuous Galerkin Methods for Convection-Diffusion Problems
    Zuozheng Zhang
    Ziqing Xie
    Zhimin Zhang
    [J]. Journal of Scientific Computing, 2009, 41 : 70 - 93
  • [9] Spacetime discontinuous Galerkin methods for convection-diffusion equations
    Sandra May
    [J]. Bulletin of the Brazilian Mathematical Society, New Series, 2016, 47 : 561 - 573
  • [10] Superconvergence of Discontinuous Galerkin Methods for Convection-Diffusion Problems
    Zhang, Zuozheng
    Xie, Ziqing
    Zhang, Zhimin
    [J]. JOURNAL OF SCIENTIFIC COMPUTING, 2009, 41 (01) : 70 - 93
12345