Γ-convergence and homogenization of functionals in Sobolev spaces with variable exponents

AbstractThis paper is devoted to homogenization and minimization problems for variational functionals in the framework of Sobolev spaces with continuous variable exponents. We assume that the sequence of exponents converges in the uniform metric and that the Lagrangian has a periodic microstructure. Then under natural coerciveness assumptions we prove a Γ-convergence result and, as a consequence, the convergence of minimizers (solutions to the corresponding Euler equations)

A homogenization result for three-phase flow though periodic heterogeneus porous media

We give homogenization results for an immiscible and incompressible three-phase ow model in a heterogeneous petroleum reservoir with periodic structure, including capillary ffects. We consider a model which leads to a coupled system of partial differential equations which includes an elliptic equation and two nonlinear degenerate parabolic equations of convection-diffusion types. Using two-scale convergence, we get an homogenized model which governs the global behavior of the ow. The determination of effective properties require the numerical resolution of local problems in a standard cell

Numerical modeling of the flow and transport of radionuclides in heterogeneous porous media

This paper is concerned with numerical methods for the modeling of flow and transport of contaminant in porous media. The numerical methods feature the mixed finite element method over triangles as a solver to the Darcy flow equation and a conservative finite volume scheme for the concentration equation. The convective term is approximated with a Godunov scheme over the dual finite volume mesh, whereas the diffusion-dispersion term is discretized by piecewise linear conforming triangular finite elements. It is shown that the scheme satisfies a discrete maximum principle. Numerical examples demonstrate the effectiveness of the methodology for a coupled system that includes an elliptic equation and a diffusion-convection-reaction equation arising when modeling flow and transport in heterogeneous porous media. The proposed scheme is robust, conservative, efficient, and stable, as confirmed by numerical simulations. © Springer Science+Business Media B.V. 2008