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

@article{Farhat2015DataAA,
  title={Data Assimilation algorithm for 3D B\'enard convection in porous media employing only temperature measurements},
  author={Aseel Farhat and Evelyn Lunasin and Edriss S. Titi},
  journal={arXiv: Analysis of PDEs},
  year={2015}
}
In this paper we propose a continuous data assimilation (downscaling) algorithm for the B\'enard convection in porous media using only coarse mesh measurements of the temperature. In this algorithm, we incorporate the observables as a feedback (nudging) term in the evolution equation of the temperature. We show that under an appropriate choice of the nudging parameter and the size of the mesh, and under the assumption that the observed data is error free, the solution of the proposed algorithm… Expand
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