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Finite element approximation of mass transfer in a porous medium with nonequilibrium phase change. (English) Zbl 1055.76030
Summary: We analyze a finite element approximation with an implicit Euler scheme. This involves numerical integration of a semi-linear parabolic-differential inclusion arising in a model of reactive mass transport in porous media with a dissolution/precipitation process. The model is composed of parabolic equations and variational inequalities. Equations are coupled by nonlinear terms. We prove existence of solutions for the approximated problem and the convergence of the scheme towards the solution of the continuous problem.

MSC:
76M10 Finite element methods applied to problems in fluid mechanics
76S05 Flows in porous media; filtration; seepage
76V05 Reaction effects in flows
49J40 Variational inequalities
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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[1] J. P. Aubin, Un Theoreme de Compacite. C. R. Acad. Sci., Paris, 1963.
[2] H. Brezis, Operateurs Maximaux Monotones et Semi-groupes de Contractions Dans Les Espaces de Hilbert. North-Holland Publishing Company, Amsterdam, 1973.
[3] P. G. Ciarlet, The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam, 1978. · Zbl 0383.65058
[4] E. Hairer and G. Wanner, Solving Ordinary Differential Equations, II. Stiff and Differentialalgebraic Problems. Springer-Verlag, New York, 1996. · Zbl 0859.65067
[5] U. Hornung, Homogenization and Porous Media. Springer, 1997. · Zbl 0872.35002
[6] DOI: 10.1137/S0036142993249024 · Zbl 0870.76039 · doi:10.1137/S0036142993249024
[7] Krizek M., East-West J. Numer. Math. 3 (1) pp 59– (1995)
[8] A., Kinetics of Geochemical Processes: Reviews of Mineralogy 8 pp 135– (1981)
[9] J.L. Lions, Quelques methodes de resolution de problemes aux limites non lineaires. Etudes Mathematiques, Dunod Gauthier-Villars, Paris, 1969.
[10] J.L. Lions and R. Dautray, Analyse Mathematique et Calcul Numerique Pour les Sciences et les Techniques, Vol. 3 of Collection du CEA. Masson, Paris, 1985. · Zbl 0642.35001
[11] E. Maisse, Analyse et simulations numeriques de phenomenes de diffusion-dissolution/ precipitation en milieux poreux, appliquees au stockage de dechets. PhD thesis, Universite Lyon 1, 1998.
[12] DOI: 10.1016/S0377-0427(97)00049-6 · Zbl 0893.76087 · doi:10.1016/S0377-0427(97)00049-6
[13] DOI: 10.1016/0377-0427(95)00192-1 · Zbl 0854.76092 · doi:10.1016/0377-0427(95)00192-1
[14] J. Pousin, A. Roukbi, R. Gourdon, P. Le Goff, and P. Moszkowicz, Evaporation d’une Substance Organique Dans un Milieu Poreux. C. R. Acad. Sci., Paris, serie IIb, 1999, Vol. 327, pp. 371 - 377. · Zbl 0921.76171
[15] DOI: 10.1137/S0036142994272866 · Zbl 0882.76040 · doi:10.1137/S0036142994272866
[16] Steefel C. I., Amer. J. Sci. 294 pp 529– (1994)
[17] F. A. Williams, Combustion Theory. Addison-Wesley, 1985.
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