Numerical discretization of a Brinkman-Darcy-Forchheimer model under singular forcing

by   Alejandro Allendes, et al.

In Lipschitz two-dimensional domains, we study a Brinkman-Darcy-Forchheimer problem on the weighted spaces 𝐇_0^1(ω,Ω) × L^2(ω,Ω)/ℝ, where ω belongs to the Muckenhoupt class A_2. Under a suitable smallness assumption, we establish the existence and uniqueness of a solution. We propose a finite element scheme and obtain a quasi-best approximation result in energy norm à la Céa under the assumption that Ω is convex. We also devise an a posteriori error estimator and investigate its reliability and efficiency properties. Finally, we design a simple adaptive strategy that yields optimal experimental rates of convergence for the numerical examples that we perform.

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