A Parallel Pressure Projection Stabilized Finite Element Method for Stokes Equation with Nonlinear Slip Boundary Conditions

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.

Author Details

Kangrui Zhou

Yueqiang Shang

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