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Error Estimates for FEM Discretizations of the Navier–Stokes Equations with Dirac Measures

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Abstract

We analyze, on two dimensional polygonal domains, classical low–order inf-sup stable finite element approximations of the stationary Navier–Stokes equations with singular sources. We operate under the assumptions that the continuous and discrete solutions are sufficiently small. We perform an a priori error analysis on convex domains. On Lipschitz, but not necessarily convex, polygonal domains, we design an a posteriori error estimator and prove its global reliability. We also explore efficiency estimates. We illustrate the theory with numerical tests.

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Authors and Affiliations

  1. GIMNAP-Departamento de Matemática, Universidad del Bío–Bío, Concepción, Chile

    Felipe Lepe

  2. Departamento de Matemática, Universidad Técnica Federico Santa María, Valparaíso, Chile

    Enrique Otárola & Daniel Quero

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  1. Felipe Lepe
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  2. Enrique Otárola
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  3. Daniel Quero
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Correspondence to Felipe Lepe.

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FL is partially supported by ANID-Chile through FONDECYT postdoctoral project 3190204 and FONDECYT project 11200529. EO is partially supported by ANID-Chile through FONDECYT project 11180193.

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Lepe, F., Otárola, E. & Quero, D. Error Estimates for FEM Discretizations of the Navier–Stokes Equations with Dirac Measures. J Sci Comput 87, 97 (2021). https://doi.org/10.1007/s10915-021-01496-x

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  • DOI: https://doi.org/10.1007/s10915-021-01496-x

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