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Volume 11, Issue 3
Two-Level Penalty Finite Element Methods for Navier-Stokes Equations with Nonlinear Slip Boundary Conditions

R. An & Y. Li

Int. J. Numer. Anal. Mod., 11 (2014), pp. 608-623.

Published online: 2014-11

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  • Abstract

The two-level penalty finite element methods for Navier-Stokes equations with nonlinear slip boundary conditions are investigated in this paper, whose variational formulation is the Navier-Stokes type variational inequality problem of the second kind. The basic idea is to solve the Navier-Stokes type variational inequality problem on a coarse mesh with mesh size $H$ in combining with solving a Stokes type variational inequality problem for simple iteration or solving a Oseen type variational inequality problem for Oseen iteration on a fine mesh with mesh size $h$. The error estimate obtained in this paper shows that if $H = O(h^{5/9})$, then the two-level penalty methods have the same convergence orders as the usual one-level penalty finite element method, which is only solving a large Navier-Stokes type variational inequality problem on the fine mesh. Hence, our methods can save an amount of computational work.

  • Keywords

Navier-Stokes Equations, Nonlinear Slip Boundary Conditions, Variational Inequality Problem, Penalty Finite Element Method, Two-Level Methods.

  • AMS Subject Headings

35Q30, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-11-608, author = {R. An and Y. Li}, title = {Two-Level Penalty Finite Element Methods for Navier-Stokes Equations with Nonlinear Slip Boundary Conditions}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2014}, volume = {11}, number = {3}, pages = {608--623}, abstract = {

The two-level penalty finite element methods for Navier-Stokes equations with nonlinear slip boundary conditions are investigated in this paper, whose variational formulation is the Navier-Stokes type variational inequality problem of the second kind. The basic idea is to solve the Navier-Stokes type variational inequality problem on a coarse mesh with mesh size $H$ in combining with solving a Stokes type variational inequality problem for simple iteration or solving a Oseen type variational inequality problem for Oseen iteration on a fine mesh with mesh size $h$. The error estimate obtained in this paper shows that if $H = O(h^{5/9})$, then the two-level penalty methods have the same convergence orders as the usual one-level penalty finite element method, which is only solving a large Navier-Stokes type variational inequality problem on the fine mesh. Hence, our methods can save an amount of computational work.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/544.html} }
TY - JOUR T1 - Two-Level Penalty Finite Element Methods for Navier-Stokes Equations with Nonlinear Slip Boundary Conditions AU - R. An & Y. Li JO - International Journal of Numerical Analysis and Modeling VL - 3 SP - 608 EP - 623 PY - 2014 DA - 2014/11 SN - 11 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/544.html KW - Navier-Stokes Equations, Nonlinear Slip Boundary Conditions, Variational Inequality Problem, Penalty Finite Element Method, Two-Level Methods. AB -

The two-level penalty finite element methods for Navier-Stokes equations with nonlinear slip boundary conditions are investigated in this paper, whose variational formulation is the Navier-Stokes type variational inequality problem of the second kind. The basic idea is to solve the Navier-Stokes type variational inequality problem on a coarse mesh with mesh size $H$ in combining with solving a Stokes type variational inequality problem for simple iteration or solving a Oseen type variational inequality problem for Oseen iteration on a fine mesh with mesh size $h$. The error estimate obtained in this paper shows that if $H = O(h^{5/9})$, then the two-level penalty methods have the same convergence orders as the usual one-level penalty finite element method, which is only solving a large Navier-Stokes type variational inequality problem on the fine mesh. Hence, our methods can save an amount of computational work.

R. An and Y. Li. (2014). Two-Level Penalty Finite Element Methods for Navier-Stokes Equations with Nonlinear Slip Boundary Conditions. International Journal of Numerical Analysis and Modeling. 11 (3). 608-623. doi:
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