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Stability of the Stokes projection on weighted spaces and applications


Authors: Ricardo G. Durán, Enrique Otárola and Abner J. Salgado
Journal: Math. Comp. 89 (2020), 1581-1603
MSC (2010): Primary 35Q35, 35Q30, 35R06, 65N15, 65N30, 76Dxx
DOI: https://doi.org/10.1090/mcom/3509
Published electronically: January 22, 2020
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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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Ricardo G. Durán
Affiliation: IMAS (UBA-CONICET) and Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, Argentina
Email: rduran@dm.uba.ar

Enrique Otárola
Affiliation: Departamento de Matemática, Universidad Técnica Federico Santa María, Valparaíso, Chile
Email: enrique.otarola@usm.cl

Abner J. Salgado
Affiliation: Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37996
Email: asalgad1@utk.edu

DOI: https://doi.org/10.1090/mcom/3509
Received by editor(s): May 2, 2019
Received by editor(s) in revised form: October 23, 2019
Published electronically: January 22, 2020
Additional Notes: The first author was partially supported by ANPCyT grant PICT 2014-1771, by CONICET grant 11220130100006CO, and by Universidad de Buenos Aires grant 20020120100050BA
The second author was partially supported by FONDECYT grant 11180193
The third author was partially supported by NSF grant DMS-1720213
Article copyright: © Copyright 2020 American Mathematical Society