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

An H1 space-time discontinuous Galerkin （STDG） scheme for convection- diffusion 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 conti...

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Bibliographic Details
Published in:Applied mathematics and mechanics 2013, Vol.34 (3), p.371-384
Main Authors: He, Siriguleng, Li, Hong, Liu, Yang
Format: Article
Language:English
Subjects:
Applications of Mathematics
Classical Mechanics
Fluid- and Aerodynamics
Galerkin方法
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Partial Differential Equations
先验误差估计
对流扩散方程
时空
有限元方法
有限差分
空间维度
间断
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Summary:An H1 space-time discontinuous Galerkin （STDG） scheme for convection- diffusion 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 exper- iments are presented to verify the theoretical results.
ISSN:0253-4827
1573-2754
DOI:10.1007/s10483-013-1677-x