Applied Mathematics and Mechanics

, Volume 29, Issue 12, pp 1579–1586 | Cite as

Mixed time discontinuous space-time finite element method for convection diffusion equations

  • Yang Liu (刘洋)Email author
  • Hong Li (李宏)
  • Siriguleng He (何斯日古楞)


A mixed time discontinuous space-time finite element scheme for secondorder convection diffusion problems is constructed and analyzed. Order of the equation is lowered by the mixed finite element method. The low order equation is discretized with a space-time finite element method, continuous in space but discontinuous in time. Stability, existence, uniqueness and convergence of the approximate solutions are proved. Numerical results are presented to illustrate efficiency of the proposed method.

Key words

convection diffusion equations mixed finite element method time discontinuous space-time finite element method convergence 

Chinese Library Classification


2000 Mathematics Subject Classification

65N30 65M60 


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  1. [1]
    Reed N H, Hill T R. Triangle mesh methods for the Neutron transport equation[R]. Report LA2 UR-73-479, Los Alamos Scientific Laboratory, 1973.Google Scholar
  2. [2]
    Cockburn B, Lin S Y. TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws III: one-dimensional systems[J]. J Comp Phys, 1989, 84(1):90–113.zbMATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    Cockburn B, Hou S C, Shu C W. TVB Runge-Kutta local projection discontinuous Galerkin method for conservation laws IV: the multidimensional case[J]. J Comp Phys, 1990, 54(3):545–581.zbMATHMathSciNetGoogle Scholar
  4. [4]
    Yan Jue, Shu Chi-wang. A local discontinuous galerkin method for KdV-type equation[R]. NASA/CR-2001-211026 ICASE, Report No.2001-20.Google Scholar
  5. [5]
    Thomée Vider. Galerkin finite element methods for parabolic problems[M]. New York: Springer-Verlag, 1997.Google Scholar
  6. [6]
    Li Hong, Guo Yan. The discontinuous space-time mixed finite element method for fourth order parabolic problems[J]. Acta Scientiarum Naturalium Universitatis NeiMongal, 2006, 37(1):20–22 (in Chinese).Google Scholar
  7. [7]
    Brezzi F, Hughes T J R, Marini L D, Masud A. Mixed discontinuous Galerkin methods for Darcy flow[J]. Journal of Scientific Computing, 2005, 22(2):119–145.CrossRefMathSciNetGoogle Scholar
  8. [8]
    Li Hong, Liu Ruxun. The space-time finite element methods for parabolic problems[J]. Applied Mathematics and Mechanics (English Edition), 2001, 22(6):687–700. DOI 10.1023/A:1016314405090zbMATHCrossRefMathSciNetGoogle Scholar
  9. [9]
    Tang Qiong, Chen Chuanmiao, Liu Luohua. Space-time finite element method for Schrödinger and its conservation[J]. Applied Mathematics and Mechanics (English Edition), 2006, 27(3): 335–340. DOI 10.1007/s10483-006-0308-2zbMATHCrossRefMathSciNetGoogle Scholar
  10. [10]
    Zhangxin chen. Finite element methods and their applications[M]. Berlin: Springer-Verlag, 2005.Google Scholar

Copyright information

© Shanghai University and Springer-Verlag GmbH 2008

Authors and Affiliations

  • Yang Liu (刘洋)
    • 1
    Email author
  • Hong Li (李宏)
    • 1
  • Siriguleng He (何斯日古楞)
    • 1
  1. 1.School of Mathematical SciencesInner Mongolia UniversityHuhhotP. R. China

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