The density dependent flow and transport problem in groundwater is solved numerically by means of a mixed finite element scheme for the flow equation and a mixed finite element-finite volume time-splitting based technique for the transport equation. The proposed approach, spatially second order accurate, is used to address the issue of grid convergence by solving on successively refined grids the salt lake problem, a physically unstable downward convection with formation of fingers. Numerical results indicate that achievement of grid convergence is problematic due to ill-conditioning arising from the strong nonlinearities of the mathematical model.