标题：Stability and superconvergence of efficient MAC schemes for fractional Stokes equation on non-uniform grids
作者：Li, Xiaoli; Rui, Hongxing; Chen, Shuangshuang
作者机构：[Li, Xiaoli; Rui, Hongxing] Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China.; [Chen, Shuangshuang] Beijing Univ Technol, BISEC, Bei 更多
通讯作者：Rui, Hongxing;Rui, HX
通讯作者地址：[Rui, HX]Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China.
来源：APPLIED NUMERICAL MATHEMATICS
关键词：MAC schemes; Time fractional Stokes equation; Stability;; Superconvergence; Efficient algorithm; Non-uniform grids
摘要：In this paper, the two MAC schemes are introduced and analyzed to solve the time fractional Stokes equation on non-uniform grids. One is the standard MAC scheme and another is the efficient MAC scheme, where the fast evaluation of the Caputo fractional derivative is used. The stability results are derived. We obtain the second order superconvergence in discrete L-2 norm for both velocity and pressure. We also obtain the second order superconvergence for some terms of the H-1 norm of the velocity on nonuniform grids. Besides, the efficient algorithm for the evaluation of the Caputo fractional derivative is used to save the storage and computation cost greatly. Finally, some numerical experiments are presented to show the efficiency and accuracy of MAC schemes. (C) 2019 IMACS. Published by Elsevier B.V. All rights reserved.