Fully discrete subgrid stabilized finite element method for the Darcy-Brinkman equations in Double-Diffusion convection

We present a fully discrete subgrid stabilized finite element method to solve the Darcy-Brinkman equations in Double-Diffusion convection. The time is advanced by one order Backward Euler scheme. With the proper choosing of stabilized parameters, the optimal error estimates in space can be obtained for velocity, temperature and concentration in H¹ semi-norm. The derived theoretical results are supported by numerical experiments. One example is to verify the convergence results and the other example is a pure thermal convection in a porous medium to verify the stability of ours method.