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Locally Stabilized Finite Element Method for Stokes Problem with Nonlinear Slip Boundary Conditions

Locally Stabilized Finite Element Method for Stokes Problem with Nonlinear Slip Boundary Conditions
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Year:    2010

Author:    Yuan Li, Kai-Tai Li

Journal of Computational Mathematics, Vol. 28 (2010), Iss. 6 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.1004-m2775

Journal of Computational Mathematics, Vol. 28 (2010), Iss. 6 : pp. 826–836

Published online:    2010-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    11

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

Author Details

Yuan Li

Kai-Tai Li

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