In this article, some local and parallel finite element methods are proposed and investigated for the time-dependent convection–diffusion problem. With backward Euler scheme for the temporal discretization, the basic idea of the present methods is that for a solution to the considered equations, 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 at each time step. The partition of unity is used to collect the local high frequency components to assemble a global continuous approximation. Theoretical results are obtained and numerical tests are reported to support the theoretical findings.

中文翻译：

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非定常对流扩散问题基于双网格离散化的局部和并行有限元方法

在本文中，针对瞬态对流扩散问题提出并研究了一些局部和并行有限元方法。对于时间离散化的后向欧拉方案，本方法的基本思想是，对于所考虑方程的解，低频分量可以通过相对粗糙的网格很好地近似，高频分量可以在精细网格上计算每个时间步都有一些本地和并行程序。统一分区用于收集局部高频分量以组装全局连续近似。获得了理论结果，并报告了数值测试以支持理论发现。