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  1. No Access

    Article

    Phase-field modeling through iterative splitting of hydraulic fractures in a poroelastic medium

    We study the propagation of hydraulic fractures using the fixed stress splitting method. The phase field approach is applied and we study the mechanics step involving displacement and phase field unknowns, with a...

    A. Mikelić, M. F. Wheeler, T. Wick in GEM - International Journal on Geomathematics (2019)

  2. No Access

    Article

    Phase-field modeling of a fluid-driven fracture in a poroelastic medium

    In this paper, we present a phase field model for a fluid-driven fracture in a poroelastic medium. In our previous work, the pressure was assumed given. Here, we consider a fully coupled system where the press...

    A. Mikelić, M. F. Wheeler, T. Wick in Computational Geosciences (2015)

  3. Article

    Special issue “Mathematics of Porous Media,” dedicated to Professor C.J. van Duijn on the occasion of his 60th anniversary

    P. Knabner, A. Mikelić, I. S. Pop in Computational Geosciences (2013)

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  4. No Access

    Chapter and Conference Paper

    Viscous Drops Spreading With Evaporation And Applications To DNA Biochips

    We develop a lubrication model for the viscous drop spreading with evaporation. It is then solved in the quasi-static case and the numerical method is used in the parameter identification in the application to...

    M. Cabrera, T. Clopeau, A. Mikelić… in Progress in Industrial Mathematics at ECMI… (2006)

  5. No Access

    Article

    Effective equations of two-phase flow in random media

    On considère le comportement des écoulements diphasiques incompressibles dans un réservoir hétérogène avec les hétérogénéités placées aléatoirement; c'est-à-dire, dans un milieux où la permeabilitéA et la porosit...

    A. Bourgeat, S. M. Kozlov, A. Mikelić in Calculus of Variations and Partial Differe… (1995)

  6. Article

    Homogenization of nonstationary Navier-Stokes equations in a domain with a grained boundary

    We prove the convergence of the homogenization process for a nonstationary Navier-Stokes system in a porous medium. The result of homogenization is Darcy's law, as in the case of the Stokes equation, but the c...

    A. Mikelić in Annali di Matematica Pura ed Applicata (1991)

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  7. No Access

    Chapter

    A Global Existence Result for the Quasistatic Frictional Contact Problem with Normal Compliance

    We consider the quasistatic problem of the contact of an elastic body with a rigid foundation in the presence of friction. The contact condition is taken as a power law normal compliance. We prove, for forces and...

    A. Klarbring, A. Mikelić, M. Shillor in Unilateral Problems in Structural Analysis IV (1991)

  8. No Access

    Article

    Duality applied to contact problems with friction

    The duality theory of Mosco, Capuzzo-Dolcetta, and Matzeu for variational and quasi-variational inequalities is extended. Then it is applied to two problems of contact with friction of an elastic body with a r...

    A. Klarbring, A. Mikelić, M. Shillor in Applied Mathematics and Optimization (1990)

  9. No Access

    Article

    Constrained kriging using quadratic programming

    N. Limić, A. Mikelić in Journal of the International Association for Mathematical Geology (1984)