A Parallel Pressure Projection Stabilized Finite Element Method for Stokes Equation with Nonlinear Slip Boundary Conditions
Year: 2020
Author: Kangrui Zhou, Yueqiang Shang
Advances in Applied Mathematics and Mechanics, Vol. 12 (2020), Iss. 6 : pp. 1438–1456
Abstract
For the low-order finite element pair $P_1-P_1$, based on full domain partition technique, a parallel pressure projection stabilized finite element algorithm for the Stokes equation with nonlinear slip boundary conditions is designed and analyzed. From the definition of the subdifferential, the variational formulation of this equation is the variational inequality problem of the second kind. Each subproblem is a global problem on the composite grid, which is easy to program and implement. The optimal error estimates of the approximate solutions are obtained by theoretical analysis since the appropriate stabilization parameter is chosen. Finally, some numerical results are given to demonstrate the high efficiency of the parallel stabilized finite element algorithm.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2019-0190
Advances in Applied Mathematics and Mechanics, Vol. 12 (2020), Iss. 6 : pp. 1438–1456
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: Stokes equations nonlinear slip boundary conditions pressure projection full domain partition parallel stabilized finite element algorithm.
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