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.
"Adaptive Double-Diffusion Model and Comparison to a Highly Heterogeneous Micro-Model." J. Appl. Math. 2012 1 - 26, 2012. https://doi.org/10.1155/2012/938727