Local and parallel finite element algorithms based on two-grid discretizations for the transient Stokes equations |
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Authors: | Yueqiang Shang Kun Wang |
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Institution: | 1.Faculty of Science,Xi’an Jiaotong University,Xi’an,People’s Republic of China;2.School of Mathematics and Computer Science,Guizhou Normal University,Guiyang,People’s Republic of China |
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Abstract: | Based on two-grid discretizations, some local and parallel finite element algorithms for the d-dimensional (d = 2,3) transient Stokes equations are proposed and analyzed. Both semi- and fully discrete schemes are considered. With backward
Euler scheme for the temporal discretization, the basic idea of the fully discrete finite element algorithms is to approximate
the generalized Stokes equations using a coarse grid on the entire domain, then correct the resulted residue using a finer
grid on overlapped subdomains by some local and parallel procedures at each time step. By the technical tool of local a priori
estimate for the fully discrete finite element solution, errors of the corresponding solutions from these algorithms are estimated.
Some numerical results are also given which show that the algorithms are highly efficient. |
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Keywords: | |
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