Journal of Applied Mathematics

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

Viviane Klein and Malgorzata Peszynska

Full-text: Open access

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.

Article information

Source
J. Appl. Math., Volume 2012 (2012), Article ID 938727, 26 pages.

Dates
First available in Project Euclid: 14 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.jam/1355495239

Digital Object Identifier
doi:10.1155/2012/938727

Mathematical Reviews number (MathSciNet)
MR2959978

Zentralblatt MATH identifier
1251.76055

Citation

Klein, Viviane; Peszynska, Malgorzata. Adaptive Double-Diffusion Model and Comparison to a Highly Heterogeneous Micro-Model. J. Appl. Math. 2012 (2012), Article ID 938727, 26 pages. doi:10.1155/2012/938727. https://projecteuclid.org/euclid.jam/1355495239


Export citation