Mixed Virtual Element-Based Numerical Schemes for Nonlinear Problems in Porous Media Flow

In this talk, we present mixed virtual element-based formulations for some nonlinear problems in porous media flow. The aim of this work is to demonstrate the capacity of these numerical schemes to approximate the variables of interest adequately. In particular, we examine the Brinkman and Navier-Stokes-Brinkman flows. The systems are formulated in terms of a pseudostress tensor and the use of Lagrange multipliers. The well-posedness of the associated augmented formulation, along with a priori error bounds for the discrete scheme, has both been established.  Finally, we provide some numerical results that confirm the theoretical results.