Analysis of a sequential regularization method for the unsteady Navier-Stokes equations

作者：Lu Xiliang^*; Lin Ping; Liu Jian Guo

来源：Mathematics of Computation, 2008, 77(263): 1467-1494.

DOI：10.1090/S0025-5718-08-02087-5

• Navier-Stokes equations
• iterative penalty method
• implicit parabolic PDE
• error estimates
• constrained dynamical system
• stabilization method

The incompressibility constraint makes Navier-Stokes equations difficult. A reformulation to a better posed problem is needed before solving it numerically. The sequential regularization method (SRM) is a reformulation which combines the penalty method with a stabilization method in the context of constrained dynamical systems and has the benefit of both methods. In the paper, we study the existence and uniqueness for the solution of the SRM and provide a simple proof of the convergence of the solution of the SRM to the solution of the Navier-Stokes equations. We also give error estimates for the time discretized SRM formulation.

• 出版日期2008