Summary
This paper is a continuation of our previous work [10] on projection methods. We study first existing “higher order” projection schemes in the semidiscretized form for the Navier-Stokes equations. One error analysis suggests that the precision of these schemes is most likely plagued by the inconsistent Neumann boundary condition satisfied by the pressure approximations. We then propose a penalty-projection scheme for which we obtain improved error estimates.
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This work is partially supported by NSF grant MS-8802596.
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Shen, J. On error estimates of some higher order projection and penalty-projection methods for Navier-Stokes equations. Numer. Math. 62, 49–73 (1992). https://doi.org/10.1007/BF01396220
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DOI: https://doi.org/10.1007/BF01396220