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Stability and convergence of efficient Navier-Stokes solvers via a commutator estimate

Jian-Guo Liu University of Maryland, College Park JIE LIU University of Maryland, College Park ROBERT L. PEGO Carnegie Mellon University

Analysis of PDEs mathscidoc:1702.03057

Communications on Pure and Applied Mathematics, 60, (10), 1443-1487, 2007.3
For strong solutions of the incompressible Navier-Stokes equations in bounded domains with velocity specified at the boundary, we establish the unconditional stability and convergence of discretization schemes that decouple the updates of pressure and velocity through explicit time stepping for pressure. These schemes require no solution of stationary Stokes systems, nor any compatibility between velocity and pressure spaces to ensure an inf-sup condition, and are representative of a class of highly efficient computational methods that have recently emerged. The proofs are simple, based upon a new, sharp estimate for the commutator of the Laplacian and Helmholtz projection operators. This allows us to treat an unconstrained formulation of the Navier-Stokes equations as a perturbed diffusion equation. © 2007 Wiley Periodicals, Inc.
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@inproceedings{jian-guo2007stability,
  title={Stability and convergence of efficient Navier-Stokes solvers via a commutator estimate},
  author={Jian-Guo Liu, JIE LIU, and ROBERT L. PEGO},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170209081544772842355},
  booktitle={Communications on Pure and Applied Mathematics},
  volume={60},
  number={10},
  pages={1443-1487},
  year={2007},
}
Jian-Guo Liu, JIE LIU, and ROBERT L. PEGO. Stability and convergence of efficient Navier-Stokes solvers via a commutator estimate. 2007. Vol. 60. In Communications on Pure and Applied Mathematics. pp.1443-1487. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170209081544772842355.
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