Convergence rates of approximations of incompressible flows through granular porous media

Abstract

We consider spectral Galerkin approximations for the strong solutions of a system of incompressible flows through granular porous medium in a bounded domain of $$\mathbb {R}^n, n=2,3$$ . We obtain uniform in time error bounds in the spatial $$L^2$$ and $$H^1$$ -norms for approximations of the velocity. Finally, we present some numerical simulations to verify the good behavior of spectral Galerkin approximations.