Pressure-robust finite element scheme for the time-dependent fully coupled Stokes-Darcy-transport problem

We present a pressure-robust mixed finite element scheme for the time -dependent fully coupled Stokes-Darcy-transport problem. The P-1(c) circle plus RT0 discretization and Raviart-Thomas mixed elements are used to discretize the velocity in the free flow region and the porous medium region, respectively. We approximate the pressure with piecewise constant finite elements and the concentration with piecewise linear finite elements. We perform a divergence-free reconstruction of the velocity in the Stokes domain. Our scheme preserves local mass conservation in the sense of projection and has pressure -robust property. The stability and error analysis of the method are obtained. The errors of velocity and concentration are independent of pressure, and our method works well even with small viscosity. The theoretical results are validated with numerical examples.