Year: 2008
Journal of Computational Mathematics, Vol. 26 (2008), Iss. 3 : pp. 410–436
Abstract
We derived and analyzed a new numerical scheme for the Navier-Stokes equations by using $H(div)$ conforming finite elements. A great deal of effort was given to an establishment of some Sobolev-type inequalities for piecewise smooth functions. In particular, the newly derived Sobolev inequalities were employed to provide a mathematical theory for the $H(div)$ finite element scheme. For example, it was proved that the new finite element scheme has solutions which admit a certain boundedness in terms of the input data. A solution uniqueness was also possible when the input data satisfies a certain smallness condition. Optimal-order error estimates for the corresponding finite element solutions were established in various Sobolev norms. The finite element solutions from the new scheme feature a full satisfaction of the continuity equation which is highly demanded in scientific computing.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2008-JCM-10360
Journal of Computational Mathematics, Vol. 26 (2008), Iss. 3 : pp. 410–436
Published online: 2008-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 27
Keywords: Finite element methods Navier-Stokes equations CFD.