Two-Level Newton Iteration Methods for Navier-Stokes Type Variational Inequality Problem

作者：An Rong^*; Qiu Hailong

来源：Advances in Applied Mathematics and Mechanics, 2013, 5(1): 36-54.

DOI：10.4208/aamm.11-m11188

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

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(vertical bar logh vertical bar H-1/2(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.

• 出版日期2013-2
• 单位温州大学