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arXiv · 2305.04427

Numerical discretizations of a convective Brinkman-Forchheimer model under singular forcing

Alejandro Allendes·Gilberto Campaña·Enrique Otarola
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Abstract

In two-dimensional Lipschitz domains, we analyze a Brinkman--Darcy--Forchheimer problem on the weighted spaces $\mathbf{H}_0^1(\omega,\Omega) \times L^2(\omega,\Omega)/\mathbb{R}$, 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 \emph{\`a la C\'ea} under the assumption that $\Omega$ 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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Alejandro Allendes, Gilberto Campaña, Enrique Otarola. 2023-05-08. Numerical discretizations of a convective Brinkman-Forchheimer model under singular forcing. https://arxiv.org/abs/2305.04427

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