A Robust and Efficient Linearization Scheme for Doubly Nonlinear and Degenerate Parabolic Problems Arising in Flow in Porous Media

Abstract

We study a nonlinear degenerate convection-diffusion model problem having an application in groundwater aquifer and petroleum reservoir simulation. The true solution typically possesses low regularity, and therefore special numerical techniques for its approximation are needed. We design a robust, efficient, and reliable linear relaxation approximation scheme. We prove the convergence of iterations at each time step in the $H^1(\Omega)$-norm. Finally, the convergence of the approximate solution in corresponding functional spaces to its exact counterpart for the parabolic problem is shown.