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In Lipschitz two-dimensional domains, we study a Brinkman-Darcy-Forchheimerproblem on the weighted spaces $\mathbf{H}_0^1(\omega,\Omega) \timesL^2(\omega,\Omega)/\mathbb{R}$, where $\omega$ belongs to the Muckenhoupt class$A_2$. Under a suitable smallness assumption, we establish the existence anduniqueness of a solution. We propose a finite element scheme and obtain aquasi-best approximation result in energy norm \`a la C\'ea under theassumption that $\Omega$ is convex. We also devise an a posteriori errorestimator and investigate its reliability and efficiency properties. Finally,we design a simple adaptive strategy that yields optimal experimental rates ofconvergence for the numerical examples that we perform.

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