Pre-Publicación 2026-15
Alonso J. Bustos, Sergio Caucao:
A posteriori error analysis of two mixed formulations for a coupled Brinkman–Forchheimer and convection-diffusion-reaction system
Abstract:
In this paper, we consider the mixed-primal and fully-mixed Banach spaces-based formulations recently proposed for the coupling of the stationary Brinkman–Forchheimer and convection-diffusion- reaction equations, and develop reliable and efficient residual-based a posteriori error estimators for both two- and three-dimensional versions of the associated mixed finite element schemes. For the reliability analysis, we employ the global inf-sup conditions associated with each uncoupled problem, combined with appropriate small data assumptions, stable Helmholtz decompositions in nonstandard Banach spaces, and the local approximation properties of the Raviart–Thomas and Clément interpolants. Efficiency is established using inverse inequalities, bubble-function localization in local L^p-spaces, and auxiliary estimates available in the literature. Finally, several numerical experiments are presented, confirming the theoretical properties of the proposed estimators and illustrating the performance of the corresponding adaptive algorithms, including the recovery of optimal convergence rates and the ability to handle challenging physical regimes.
