Finite element approximation of mass transfer in a porous medium with non equilibrium phase change

A finite element approximations with an implicit Euler scheme is analyzed. 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 non-linear terms. We prove the existence of solutions for the approximated problem and the convergence of the scheme towards the solution of the continuous Problem

[1]  R. Dautray,et al.  Analyse mathématique et calcul numérique pour les sciences et les techniques , 1984 .

[2]  E. Boschi.  Recensioni: J. L. Lions - Quelques méthodes de résolution des problémes aux limites non linéaires. Dunod, Gauthier-Vi;;ars, Paris, 1969; , 1971 .

[3]  Jérôme Pousin,et al.  Diffusion and dissolution/precipitation in an open porous reactive medium , 1997 .

[4]  H. Brezis.  Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert , 1973 .

[5]  Philippe G. Ciarlet,et al.  The finite element method for elliptic problems , 2002, Classics in applied mathematics.

[6]  Richard E. Ewing,et al.  Stability and Convergence of a Finite Element Method for Reactive Transport in Ground Water , 1997 .

[7]  U. Hornung.  Homogenization and porous media , 1996 .

[8]  C. Steefel,et al.  A coupled model for transport of multiple chemical species and kinetic precipitation/dissolution rea , 1994 .

[9]  E. Hairer,et al.  Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems , 2010 .

[10]  J. Lions.  Quelques méthodes de résolution de problèmes aux limites non linéaires , 1969 .

[11]  Jérôme Pousin,et al.  Diffusion and dissolution in a reactive porous medium: mathematical modelling and numerical simulations , 1996 .

[12]  E. Hairer,et al.  Solving Ordinary Differential Equations I , 1987 .

[13]  John W. Barrett,et al.  Finite Element Approximation of the Transport of Reactive Solutes in Porous Media. Part 1: Error Estimates for Nonequilibrium Adsorption Processes , 1997 .

[14]  Jérôme Pousin,et al.  Évaporation d'une substance organique dans un milieu poreux , 1999 .