Year: 2013
Author: Rong An, Hailong Qiu
Advances in Applied Mathematics and Mechanics, Vol. 5 (2013), Iss. 1 : pp. 36–54
Abstract
This paper deals with the two-level Newton iteration method based on the pressure projection stabilized finite element approximation to solve the numerical solution of the Navier-Stokes type variational inequality problem. We solve a small Navier-Stokes problem on the coarse mesh with mesh size $H$ and solve a large linearized Navier-Stokes problem on the fine mesh with mesh size $h$. The error estimates derived show that if we choose $h=\mathcal{O}(|\log h|^{1/2}H^3)$, then the two-level method we provide has the same $H^1$ and $L^2$ convergence orders of the velocity and the pressure as the one-level stabilized method. However, the $L^2$ convergence order of the velocity is not consistent with that of one-level stabilized method. Finally, we give the numerical results to support the theoretical analysis.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.11-m11188
Advances in Applied Mathematics and Mechanics, Vol. 5 (2013), Iss. 1 : pp. 36–54
Published online: 2013-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: Navier-Stokes equations nonlinear slip boundary conditions variational inequality problem stabilized finite element two-level methods.
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