Convergence analysis for a conformal discretization of a model for precipitation and dissolution in porous media

In this paper we discuss the numerical analysis of an upscaled (core scale) model describing the transport, precipitation and dissolution of solutes in a porous medium. The particularity lies in the modeling of the reaction term, especially the dissolution term, which has a multivalued character. We...

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Bibliographic Details
Published inNumerische Mathematik Vol. 127; no. 4; pp. 715 - 749
Main Authors Kumar, K., Pop, I. S., Radu, F. A.
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2014
Subjects
adsorption processes
crystal dissolution
diffusion
equations
equilibrium
Finite-element discretization
flows
Matematik
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Numerical Analysis
Numerical and Computational Physics
reactive solute transport
scheme
Simulation
Theoretical
65L60
35A35
65J20
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Summary:In this paper we discuss the numerical analysis of an upscaled (core scale) model describing the transport, precipitation and dissolution of solutes in a porous medium. The particularity lies in the modeling of the reaction term, especially the dissolution term, which has a multivalued character. We consider the weak formulation for the upscaled equation and provide rigorous stability and convergence results for both the semi-discrete (time discretization) and the fully discrete schemes. In doing so, compactness arguments are employed.
ISSN:0029-599X
0945-3245
0945-3245
DOI:10.1007/s00211-013-0601-1