The Penalty resolution of the spectral element discretization of the time dependent Darcy equations

The time-dependent Darcy system, when discretized in time using the implicit Euler scheme and in space using the spectral element method, can be efficiently solved using the penalty method. This approach allows the decoupling of the computations for velocity and pressure. We also derive a priori error estimates for the spectral element discretization of the time-dependent Darcy equations.