Abstract
Based on two-grid discretizations, local and parallel finite element algorithms are proposed and analyzed for the time-dependent Oseen equations. Using conforming finite element pairs for the spatial discretization and backward Euler scheme for the temporal discretization, the basic idea of the fully discrete finite element algorithms is to approximate the generalized Oseen equations using a coarse grid on the entire domain, and then correct the resulted residual using a fine grid on overlapped subdomains by some local and parallel procedures at each time step. By the theoretical tool of local a priori estimate for the fully discrete finite element solution, error bounds of the approximate solutions from the algorithms are estimated. Numerical results are also given to demonstrate the efficiency of the algorithms.
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Acknowledgments
The authors would like to express their deep gratitude to the anonymous reviewers for their valuable comments and suggestions, which led to an improvement of the paper.
Funding
This work was supported by the Natural Science Foundation of China (No.11361016), the Basic and Frontier Explore Program of Chongqing Municipality, China (No. cstc2018jcyjAX0305), the Fundamental Research Funds for the Central Universities (No. XDJK2018B032), and the Graduate Research Innovation Project of Chongqing Municipality, China (No. CYS19085).
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Ding, Q., Zheng, B. & Shang, Y. Local and parallel finite element algorithms for the time-dependent Oseen equations. Numer Algor 87, 1653–1677 (2021). https://doi.org/10.1007/s11075-020-01024-2
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DOI: https://doi.org/10.1007/s11075-020-01024-2