  In this work we develop an a posteriori error analysis of a conforming mixed
finite element method for solving the coupled problem arising in the
interaction between a free fluid and a fluid in a poroelastic medium on
isotropic meshes in $\mathbb{R}^d$, $d\in\{2,3\}$. The approach utilizes the
semi-discrete formulation proposed by Ilona Ambartsumyan et al. in (Numerische
Mathematik, October 2017). The a posteriori error estimate is based on a
suitable evaluation on the residual of the finite element solution. It is
proven that the a posteriori error estimate provided in this paper is both
reliable and efficient. The proof of reliability makes use of suitable
auxiliary problems, diverse continuous inf-sup conditions satisfied by the
bilinear forms involved, Helmholtz decomposition, and local approximation
properties of the Cl\'ement interpolant. On the other hand, inverse
inequalities, and the localization technique based on simplexe-bubble and
face-bubble functions are the main tools for proving the efficiency of the
estimator. Up to minor modifications, our analysis can be extended to other
finite element subspaces yielding a stable Galerkin scheme.
