Adaptive Double‐Diffusion Model and Comparison to a Highly Heterogeneous Micro‐Model
Viviane Klein, Małgorzata Peszyńska · Journal of Applied Mathematics · 2012
Double‐diffusion model is used to simulate slightly compressible fluid flow in periodic porous media as a macro‐model in place of the original highly heterogeneous micro‐model. In this paper, we formulate an adaptive two‐grid numerical finite element discretization of the double‐diffusion system and perform a comparison between the micro‐ and macro‐model. Our numerical results show that the micro‐model solutions appear to converge to the macro‐model linearly with the parameter ε of periodic geometry. For the two‐grid discretization, the a priori and a posteriori error estimates are proved, and we show how to adapt the grid for each component independently.