Adaptive double-diffusion model and comparison to a highly heterogeneous micro-model

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. © 2012 viviane klein and malgorzata peszynska.