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Numerische Mathematik

, Volume 127, Issue 4, pp 715–749 | Cite as

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

  • K. Kumar
  • I. S. PopEmail author
  • F. A. Radu
Article

Abstract

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.

Mathematics Subject Classification

35A35 65L60 65J20 

Notes

Acknowledgments

K. Kumar would like to thank the Technology Foundation STW for the financial support through the Project 07796, “Second Generation of Integrated Batteries”. The authors are members of the International Research Training Group NUPUS funded by the German Research Foundation DFG (GRK 1398) and by the Netherlands Organisation for Scientific Research NWO (DN 81-754). Part of the work was carried out when K. Kumar visited the Institute of Mathematics, University of Bergen. The support is gratefully acknowledged. K. Kumar would also like to thank Dr. Thomas Wick and Dr. Ahmed El Sheikh (UT Austin) for their feedback on the numerical computations. F.A. Radu acknowledges the support of Statoil through the Akademia Grant 2012–2013.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Center for Subsurface ModelingThe University of Texas at AustinAustinUSA
  2. 2.Department of Mathematics and Computer ScienceEindhoven University of TechnologyEindhovenThe Netherlands
  3. 3.Institute of MathematicsUniversity of BergenBergenNorway

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