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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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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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Additional Information
  • Ricardo G. Durán
  • Affiliation: IMAS (UBA-CONICET) and Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, Argentina
  • ORCID: 0000-0003-1349-3708
  • 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
  • MR Author ID: 847180
  • Email: asalgad1@utk.edu
  • 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
  • © Copyright 2020 American Mathematical Society
  • Journal: Math. Comp. 89 (2020), 1581-1603
  • MSC (2010): Primary 35Q35, 35Q30, 35R06, 65N15, 65N30, 76Dxx
  • DOI: https://doi.org/10.1090/mcom/3509
  • MathSciNet review: 4081912