Volume 5, Issue 1
Two-Level Newton Iteration Methods for Navier-Stokes Type Variational Inequality Problem

Rong An & Hailong Qiu

Adv. Appl. Math. Mech., 5 (2013), pp. 36-54.

Published online: 2013-05

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  • 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=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.

  • Keywords

Navier-Stokes equations nonlinear slip boundary conditions variational inequality problem stabilized finite element two-level methods

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COPYRIGHT: © Global Science Press

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