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Volume 28, Issue 6
Locally Stabilized Finite Element Method for Stokes Problem with Nonlinear Slip Boundary Conditions

Yuan Li & Kai-Tai Li

DOI: 10.4208/jcm.1004-m2775

J. Comp. Math., 28 (2010), pp. 826-836.

Published online: 2010-12

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  • Abstract

Based on the low-order conforming finite element subspace $(V_h,M_h)$ such as the $P_1$-$P_0$ triangle element or the $Q_1$-$P_0$ quadrilateral element, the locally stabilized finite element method for the Stokes problem with nonlinear slip boundary conditions is investigated in this paper. For this class of nonlinear slip boundary conditions including the subdifferential property, the weak variational formulation associated with the Stokes problem is an variational inequality. Since $(V_h,M_h)$ does not satisfy the discrete inf-sup conditions, a macroelement condition is introduced for constructing the locally stabilized formulation such that the stability of $(V_h,M_h)$ is established. Under these conditions, we obtain the $H^1$ and $L^2$ error estimates for the numerical solutions.

  • Keywords

Stokes Problem, Nonlinear Slip Boundary, Variational Inequality, Local Stabilized Finite Element Method, Error Estimate.

  • AMS Subject Headings

35Q30.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-28-826, author = { , Yuan Li and Li , Kai-Tai}, title = {Locally Stabilized Finite Element Method for Stokes Problem with Nonlinear Slip Boundary Conditions}, journal = {Journal of Computational Mathematics}, year = {2010}, volume = {28}, number = {6}, pages = {826--836}, abstract = {

Based on the low-order conforming finite element subspace $(V_h,M_h)$ such as the $P_1$-$P_0$ triangle element or the $Q_1$-$P_0$ quadrilateral element, the locally stabilized finite element method for the Stokes problem with nonlinear slip boundary conditions is investigated in this paper. For this class of nonlinear slip boundary conditions including the subdifferential property, the weak variational formulation associated with the Stokes problem is an variational inequality. Since $(V_h,M_h)$ does not satisfy the discrete inf-sup conditions, a macroelement condition is introduced for constructing the locally stabilized formulation such that the stability of $(V_h,M_h)$ is established. Under these conditions, we obtain the $H^1$ and $L^2$ error estimates for the numerical solutions.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1004-m2775}, url = {http://global-sci.org/intro/article_detail/jcm/8552.html} }
TY - JOUR T1 - Locally Stabilized Finite Element Method for Stokes Problem with Nonlinear Slip Boundary Conditions AU - , Yuan Li AU - Li , Kai-Tai JO - Journal of Computational Mathematics VL - 6 SP - 826 EP - 836 PY - 2010 DA - 2010/12 SN - 28 DO - http://doi.org/10.4208/jcm.1004-m2775 UR - https://global-sci.org/intro/article_detail/jcm/8552.html KW - Stokes Problem, Nonlinear Slip Boundary, Variational Inequality, Local Stabilized Finite Element Method, Error Estimate. AB -

Based on the low-order conforming finite element subspace $(V_h,M_h)$ such as the $P_1$-$P_0$ triangle element or the $Q_1$-$P_0$ quadrilateral element, the locally stabilized finite element method for the Stokes problem with nonlinear slip boundary conditions is investigated in this paper. For this class of nonlinear slip boundary conditions including the subdifferential property, the weak variational formulation associated with the Stokes problem is an variational inequality. Since $(V_h,M_h)$ does not satisfy the discrete inf-sup conditions, a macroelement condition is introduced for constructing the locally stabilized formulation such that the stability of $(V_h,M_h)$ is established. Under these conditions, we obtain the $H^1$ and $L^2$ error estimates for the numerical solutions.

Yuan Li & Kai-Tai Li. (1970). Locally Stabilized Finite Element Method for Stokes Problem with Nonlinear Slip Boundary Conditions. Journal of Computational Mathematics. 28 (6). 826-836. doi:10.4208/jcm.1004-m2775
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