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In this paper we propose a continuous data assimilation (downscaling)algorithm for the B\'enard convection in porous media using only coarse meshmeasurements of the temperature. In this algorithm, we incorporate theobservables as a feedback (nudging) term in the evolution equation of thetemperature. We show that under an appropriate choice of the nudging parameterand the size of the mesh, and under the assumption that the observed data iserror free, the solution of the proposed algorithm converges at an exponentialrate, asymptotically in time, to the unique exact unknown reference solution ofthe original system, associated with the observed (finite dimensionalprojection of) temperature data. Moreover, we note that in the case where theobservational measurements are not error free, one can estimate the errorbetween the solution of the algorithm and the exact reference solution of thesystem in terms of the error in the measurements.

Data Assimilation algorithm for 3D B\'enard convection in porous media employing only temperature measurements