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Applied Mathematics and Mechanics (English Edition) ›› 2013, Vol. 34 ›› Issue (3): 371-384.doi: https://doi.org/10.1007/s10483-013-1677-x

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H1 space-time discontinuous finite element method for convection-diffusion equations

何斯日古楞 李宏 刘洋   

  1. School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, P. R. China
  • 收稿日期:2012-02-27 修回日期:2012-09-27 出版日期:2013-03-03 发布日期:2013-02-06
  • 通讯作者: Hong LI, Professor, Ph.D., E-mail: malhong@imu.edu.cn E-mail:malhong@imu.edu.cn

H1  space-time discontinuous finite element method for convection-diffusion equations

Siriguleng HE, Hong LI, Yang LIU   

  1. School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, P. R. China
  • Received:2012-02-27 Revised:2012-09-27 Online:2013-03-03 Published:2013-02-06
  • Contact: Hong LI, Professor, Ph.D., E-mail: malhong@imu.edu.cn E-mail:malhong@imu.edu.cn

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摘要： An H1 space-time discontinuous Galerkin (STDG) scheme for convectiondiffusion equations in one spatial dimension is constructed and analyzed. This method is formulated by combining the H1   Galerkin method and the space-time discontinuous finite element method that is discontinuous in time and continuous in space. The existence and the uniqueness of the approximate solution are proved. The convergence of the scheme is analyzed by using the techniques in the finite difference and finite element methods. An optimal a-priori error estimate in the L∞(H1  ) norm is derived. The numerical experiments are presented to verify the theoretical results.

关键词: foamed aluminum, drainage, Plateau border, liquid holdup, pentagonal dodecahedron, convection-diffusion equation, error estimate, space-time discontinuous finite element method, H1  method

Abstract: An H1 space-time discontinuous Galerkin (STDG) scheme for convectiondiffusion equations in one spatial dimension is constructed and analyzed. This method is formulated by combining the H1 Galerkin method and the space-time discontinuous finite element method that is discontinuous in time and continuous in space. The existence and the uniqueness of the approximate solution are proved. The convergence of the scheme is analyzed by using the techniques in the finite difference and finite element methods. An optimal a-priori error estimate in the L∞(H1 ) norm is derived. The numerical experiments are presented to verify the theoretical results.

Key words: foamed aluminum, drainage, Plateau border, liquid holdup, pentagonal dodecahedron, error estimate, H1 method, convection-diffusion equation, space-time discontinuous finite element method

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