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In this work we develop an a posteriori error analysis of a conforming mixedfinite element method for solving the coupled problem arising in theinteraction between a free fluid and a fluid in a poroelastic medium onisotropic meshes in $\mathbb{R}^d$, $d\in\{2,3\}$. The approach utilizes thesemi-discrete formulation proposed by Ilona Ambartsumyan et al. in (NumerischeMathematik, October 2017). The a posteriori error estimate is based on asuitable evaluation on the residual of the finite element solution. It isproven that the a posteriori error estimate provided in this paper is bothreliable and efficient. The proof of reliability makes use of suitableauxiliary problems, diverse continuous inf-sup conditions satisfied by thebilinear forms involved, Helmholtz decomposition, and local approximationproperties of the Cl\'ement interpolant. On the other hand, inverseinequalities, and the localization technique based on simplexe-bubble andface-bubble functions are the main tools for proving the efficiency of theestimator. Up to minor modifications, our analysis can be extended to otherfinite element subspaces yielding a stable Galerkin scheme.

A posteriori error analysis for a Lagrange multiplier method for a Stokes/Biot fluid-poroelastic structure interaction model