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In this work we derive a posteriori error estimates for theconvection-diffusion-reaction equation coupled with the Darcy-Forchheimerproblem by a nonlinear external source depending on the concentration of thefluid. We introduce the variational formulation associated to the problem, anddiscretize it by using the finite element method. We prove optimal a posteriorierrors with two types of calculable error indicators. The first one is linkedto the linearization and the second one to the discretization. Then we findupper and lower error bounds under additional regularity assumptions on theexact solutions. Finally, numerical computations are performed to show theeffectiveness of the obtained error indicators.

A Posteriori error estimates for Darcy-Forchheimer's problem coupled with the convection-diffusion-reaction equation