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

Xiliang Lu National University of Singapore Ping Lin National University of Singapore Jian-Guo Liu University of Maryland

Numerical Analysis and Scientific Computing mathscidoc:1702.25038

Mathematics of Computation, 77, (263), 1467–1494, 2008.7
he 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.
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@inproceedings{xiliang2008analysis,
  title={Analysis of a sequential regularization method for the unsteady Navier-Stokes equations},
  author={Xiliang Lu, Ping Lin, and Jian-Guo Liu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170209010108164076352},
  booktitle={Mathematics of Computation},
  volume={77},
  number={263},
  pages={1467–1494},
  year={2008},
}
Xiliang Lu, Ping Lin, and Jian-Guo Liu. Analysis of a sequential regularization method for the unsteady Navier-Stokes equations. 2008. Vol. 77. In Mathematics of Computation. pp.1467–1494. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170209010108164076352.
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