Stability of the Stokes projection on weighted spaces and applications
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2019
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| _version_ | 1866908599611031552 |
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| author | Duran, Ricardo G. Otarola, Enrique Salgado, Abner J. |
| author_facet | Duran, Ricardo G. Otarola, Enrique Salgado, Abner J. |
| contents | We show that, on convex polytopes and two or three dimensions, the finite element Stokes projection is stable on weighted spaces $\mathbf{W}^{1,p}_0(ω,Ω) \times L^p(ω,Ω)$, 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1905_00476 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Stability of the Stokes projection on weighted spaces and applications Duran, Ricardo G. Otarola, Enrique Salgado, Abner J. Numerical Analysis 35Q35, 35Q30, 35R06, 65N15, 65N30, 76Dxx We show that, on convex polytopes and two or three dimensions, the finite element Stokes projection is stable on weighted spaces $\mathbf{W}^{1,p}_0(ω,Ω) \times L^p(ω,Ω)$, 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. |
| title | Stability of the Stokes projection on weighted spaces and applications |
| topic | Numerical Analysis 35Q35, 35Q30, 35R06, 65N15, 65N30, 76Dxx |
| url | https://arxiv.org/abs/1905.00476 |