Maximum-principle-satisfying second order discontinuous Galerkin schemes for convection–diffusion equations on triangular meshes
作者: Yifan ZhangXiangxiong ZhangChi-Wang Shu
作者单位: 1Division of Applied Mathematics, Brown University, Providence, RI 02912, United States
2Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, United States
刊名: Journal of Computational Physics, 2013, Vol.234 , pp.295-316
来源数据库: Elsevier Journal
DOI: 10.1016/j.jcp.2012.09.032
关键词: Discontinuous Galerkin methodMaximum principlePositivity preservingConvection–diffusion equationsIncompressible Navier–Stokes equationsDegenerate parabolic equationsTriangular meshes
英文摘要: Abstract(#br)We propose second order accurate discontinuous Galerkin (DG) schemes which satisfy a strict maximum principle for general nonlinear convection–diffusion equations on unstructured triangular meshes. Motivated by genuinely high order maximum-principle-satisfying DG schemes for hyperbolic conservation laws (Perthame, 1996) and (Zhang, 2010) [14,26], we prove that under suitable time step restriction for forward Euler time stepping, for general nonlinear convection–diffusion equations, the same scaling limiter coupled with second order DG methods preserves the physical bounds indicated by the initial condition while maintaining uniform second order accuracy. Similar to the purely convection cases, the limiters are mass conservative and easy to implement. Strong stability...
全文获取路径: Elsevier  (合作)
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影响因子:2.138 (2012)

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关键词翻译
关键词翻译
  • convection 对流
  • triangular 三角形的
  • principle 原理
  • satisfying 饱和
  • diffusion 扩散
  • preserving 保藏
  • discontinuous 不连续的
  • parabolic 抛物线的
  • order 
  • second