Local and Parallel Finite Element Algorithms for the Time-Dependent Convection-Diffusion Equations
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摘要: 对基于两重网格的非定常对流扩散方程的局部和并行有限元算法进行了研究．算法的理论依据是两重网格的思想，解的低频分量可以用一个整体的粗网格空间来逼近，高频分量可以用局部和并行的细网格空间来逼近．因此，这种局部和并行算法仅仅涉及一个粗网格上的整体逼近和细网格上的局部校正．得到了算法的误差估计，一些数值例子验证了算法的有效性．Abstract: Local and parallel finite element algorithms based on two-grid discretization for the timedependent convection-diffusion equations are presented.These algorithms are motivated by the observation that for a solution to the convection-diffusion problems,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 procedure.Hence,these local and parallel algorithms only involve one small original problem on coarse mesh and some correction problems on local fine grid.One technical tool for the analysis is some local a priori estimates that are also obtained.Finally,some numerical examples are given to support our theoretical analysis.
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