In this paper, we carry out an a posteriori error analysis of Legendre spectral
approximations to the Stokes/Darcy coupled equations. The spectral approximations
are based on a weak formulation of the coupled equations by using the Beavers-Joseph-
Saffman interface condition. The main contribution of the paper consists of deriving
a number of posteriori error indicators and their upper and lower bounds for the sin-
gle domain case. An extension of the upper bounds to the multi-domain case in the
spectral element framework is also given.