Volume 12, Issue 6
A Parallel Pressure Projection Stabilized Finite Element Method for Stokes Equation with Nonlinear Slip Boundary Conditions

Adv. Appl. Math. Mech., 12 (2020), pp. 1438-1456.

Published online: 2020-09

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• 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.

• Keywords

Stokes equations, nonlinear slip boundary conditions, pressure projection, full domain partition, parallel stabilized finite element algorithm.

68W10, 76M10, 76D07

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@Article{AAMM-12-1438, author = {Zhou , Kangrui and Shang , Yueqiang}, title = {A Parallel Pressure Projection Stabilized Finite Element Method for Stokes Equation with Nonlinear Slip Boundary Conditions}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2020}, volume = {12}, number = {6}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2019-0190}, url = {http://global-sci.org/intro/article_detail/aamm/18295.html} }
TY - JOUR T1 - A Parallel Pressure Projection Stabilized Finite Element Method for Stokes Equation with Nonlinear Slip Boundary Conditions AU - Zhou , Kangrui AU - Shang , Yueqiang JO - Advances in Applied Mathematics and Mechanics VL - 6 SP - 1438 EP - 1456 PY - 2020 DA - 2020/09 SN - 12 DO - http://doi.org/10.4208/aamm.OA-2019-0190 UR - https://global-sci.org/intro/article_detail/aamm/18295.html KW - Stokes equations, nonlinear slip boundary conditions, pressure projection, full domain partition, parallel stabilized finite element algorithm. AB -

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.

Kangrui Zhou & Yueqiang Shang. (2020). A Parallel Pressure Projection Stabilized Finite Element Method for Stokes Equation with Nonlinear Slip Boundary Conditions. Advances in Applied Mathematics and Mechanics. 12 (6). 1438-1456. doi:10.4208/aamm.OA-2019-0190
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