Positive vertex finite volume schemes for degenerate parabolic equations arising in porous media flow models

El Houssaine Quenjel
Laboratoire Jean Dieudonné Nice
Jeudi, 12 Septembre, 2019 - 11:00 - 12:00

My talk will be centered on the control volume finite element method for the approximation of solutions to degenerate convection-diffusion equations. The main point consists in designing a discretization which allows to ensure both the positivity and the coercivity of the numerical scheme. The idea is essentially based on appropriate upwind approximations of the fluxes. A particular emphasize is placed on the convergence of the method while the discrete solution stays physically admissible. Taking also into account accuracy quests, I will present several propositions that retain the mentioned ingredients. Moreover, the approach is successfully applied to a simple diffusion equation. Numerical tests are presented in order to validate the expected results. Next, I will extend the methodology to a challenging system modeling compressible flows in porous media. Finally, I will conclude my presentation with some perspectives on the topic.