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Finite Element Discretizations of a Convective Brinkman–Forchheimer Model Under Singular Forcing

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Abstract

In two-dimensional bounded Lipschitz domains, we analyze a convective Brinkman–Forchheimer problem on the weighted spaces \({{\textbf {H}}}_0^1(\omega ,\varOmega ) \times L^2(\omega ,\varOmega )/{\mathbb {R}}\), where \(\omega \) belongs to the Muckenhoupt class \(A_2\). Under a suitable smallness assumption, we prove the existence and uniqueness of a solution. We propose a finite element method and obtain a quasi-best approximation result in the energy norm à la Céa under the assumption that \(\varOmega \) is convex. We also develop an a posteriori error estimator and study its reliability and efficiency properties. Finally, we develop an adaptive method that yields optimal experimental convergence rates for the numerical examples we perform.

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The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Funding

AA is partially supported by ANID through FONDECYT project 1210729. GC is partially supported by ANID–Subdirección de Capital Humano/Doctorado Nacional/2020-21200920. EO is partially supported by ANID through FONDECYT project 1220156.

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  1. Departamento de Matemática, Universidad Técnica Federico Santa María, Valparaiso, Chile

    Alejandro Allendes & Enrique Otárola

  2. Departamento de Ciencias, Universidad Técnica Federico Santa María, Valparaiso, Chile

    Gilberto Campaña

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  1. Alejandro Allendes
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Allendes, A., Campaña, G. & Otárola, E. Finite Element Discretizations of a Convective Brinkman–Forchheimer Model Under Singular Forcing. J Sci Comput 99, 58 (2024). https://doi.org/10.1007/s10915-024-02513-5

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