Local and parallel finite element algorithms for time-dependent convection-diffusion equations

Local and parallel finite element algorithms based on two-grid discretization for the time-dependent convection-diffusion equations are presented. These algorithms are motivated by the observation that, for a solution to the convection-diffusion problem, low frequency components can be approximated...

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Bibliographic Details
Published in:Applied mathematics and mechanics 2009-06, Vol.30 (6), p.787-794
Main Authors: Liu, Qing-fang, Hou, Yan-ren
Format: Article
Language:English
Subjects:
Algorithms
Applications of Mathematics
Approximation
Classical Mechanics
Convection-diffusion equation
Discretization
Finite element method
Fluid- and Aerodynamics
Mathematical analysis
Mathematical Modeling and Industrial Mathematics
Mathematical models
Mathematics
Mathematics and Statistics
Partial Differential Equations
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Summary:Local and parallel finite element algorithms based on two-grid discretization for the time-dependent convection-diffusion equations are presented. These algorithms are motivated by the observation that, for a solution to the convection-diffusion problem, low frequency components can be approximated well by a relatively coarse grid and high frequency components can be computed on a fine grid by some local and parallel procedures. Hence, these local and parallel algorithms only involve one small original problem on the coarse mesh and some correction problems on the local fine grid. One technical tool for the analysis is the local a priori estimates that are also obtained. Some numerical examples are given to support our theoretical analysis.
ISSN:0253-4827
1573-2754
DOI:10.1007/s10483-009-0613-x