Abstract

In two-dimensional bounded Lipschitz domains, we analyze a convective Brinkman–Forchheimer problem on the weighted spaces H01(?,?)×L2(?,?)/R, where ? belongs to the Muckenhoupt class A2. 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 ? 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. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.