Abstract
An adaptive local postprocessing finite element method for the Navier-Stokes equations is presented in this paper. We firstly solve the problem on a relative coarse grid to get a rough approximation. Then, we correct the rough approximation by solving a series of approximate local residual equations defined on some local fine grids, which can be implemented in parallel. In addition, we also propose a reliable local a posteriori error estimator and construct an adaptive algorithm based on the corresponding a posterior error estimate. Finally, some numerical examples are presented to verify the algorithm.
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Supported by NSF of China (Grant No. 11171269 and 11001216) and PhD Programs Foundation of Ministry of Education of China (Grant No. 20110201110027).
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Song, L., Hou, Y. & Zheng, H. Adaptive Local Postprocessing Finite Element Method for the Navier-Stokes Equations. J Sci Comput 55, 255–267 (2013). https://doi.org/10.1007/s10915-012-9631-6
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DOI: https://doi.org/10.1007/s10915-012-9631-6