Local and parallel finite element algorithms for the stokes problem
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- He, Y., Xu, J., Zhou, A. et al. Numer. Math. (2008) 109: 415. doi:10.1007/s00211-008-0141-2
Based on two-grid discretizations, some local and parallel finite element algorithms for the Stokes problem are proposed and analyzed in this paper. These algorithms are motivated by the observation that for a solution to the Stokes problem, 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. One technical tool for the analysis is some local a priori estimates that are also obtained in this paper for the finite element solutions on general shape-regular grids.