A discontinuous in time Streamline Diffusion Virtual Element Method for Darcy-transport problem

We present a first numerical study of transport phenomena involving chemically reactive species, modeled by advection-diffusion-reaction systems with flow fields governed by Darcy's law. Among the various discretisation approaches, we consider the Streamline Diffusion method. Both the velocity field and the species concentrations are computed using the Virtual Element Method using a Discontinuous Galerkin scheme for time. An abstract error estimate has been derived using a special technique that utilizes Gauss-Radau interpolation in conjunction with numerical integration. These theoretical findings are supported by numerical experiments with arbitrary-order accuracy in both space and time.