Adaptive Double-Diffusion Model and Comparison to a Highly Heterogeneous Micro-Model

Viviane Klein and Malgorzata Peszynska

Journal of Applied Mathematics, 2012, vol. 2012, 1-26

Abstract:

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.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:938727

DOI: 10.1155/2012/938727

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