Saltwater, or brine, underlies freshwater in many aquifers, with a transition zone separating them. Pumping freshwater by a well located above the transition zone produces upconing of the latter, eventually salinizing the pumped water, forcing shut-off. Following the well's shut-off, the upconed saltwater mound undergoes decay, tending to return to the pre-pumping regime. The FEAS code is used for the simulation of coupled density-dependent flow and salt transport involved in the upconing-decay process. In this code, the flow equation is solved by the Galerkin finite element method (FEM), while the advective-dispersive salt transport equation is solved in the Eulerian-Lagrangian framework. The code does not suffer from the instability constraint on the Peclet number. The code is used to investigate the transient upconing-decay process in an axially symmetric system and to discover how the process is affected by two major factors: the density difference factor (DDF) and the dispersivities. Simulation results show that under certain conditions, pumping essentially freshwater can be maintained for a certain time period, the length of which depends on the dispersivity values used. A recirculating flow cell may occur in the saltwater layer beneath the pumping well, widening the saltwater mound. The decay process is lengthy; it takes a long time for the upconed saltwater to migrate back to its original shape of a horizontal transition zone prior to pumping. However, the wider transition zone caused by hydrodynamic dispersion can never return to the initial one. This indicates that once a pumping well is abandoned because of high salinity, it can be reused for groundwater utilization only after a long time. It is also shown that the upconing-decay process is very sensitive to DDF, which, in our work, ranges from 0 (for an ideal tracer) to 0.2 (for brine). For a DDF of 0.025 (for seawater), local upconing occurs only for low iso-salinity surfaces, while those of high salt concentration remain stable after a short time. For an ideal tracer, all iso-salinity surfaces rise toward the pumping well, whereas for brine only iso-salinity surfaces of very low salinity upcone towards the pumping well. This may imply that the traditional finding that the sharp interface approximation is practically close to the 0.5 iso-salinity surface may not be true for a high DDF solution.