Stability of the Stokes projection on weighted spaces and applications

Durán, Ricardo; Otárola, Enrique; Salgado, Abner

doi:10.1090/mcom/3509

Stability of the Stokes projection on weighted spaces and applications
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by Ricardo G. Durán, Enrique Otárola and Abner J. Salgado HTML | PDF

Math. Comp. 89 (2020), 1581-1603 Request permission

Abstract:

We show that on convex polytopes in two or three dimensions, the finite element Stokes projection is stable on weighted spaces ${\mathbf {W}}^{1,p}_0(\omega ,\Omega ) \times L^p(\omega ,\Omega )$, where the weight belongs to a certain Muckenhoupt class and the integrability index can be different from two. We show how this estimate can be applied to obtain error estimates for approximations of the solution to the Stokes problem with singular sources.

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