We have used a finite element model of time-dependent convection to determine the conditions for penetration of the subducted plate into the lower mantle. A temperature-dependent and non-Newtonian rheology is applied to achieve platelike behavior of the upper and sinking thermal boundary layer of convection. The 650-km discontinuity is taken as either a chemical or phase boundary or as a combination of both. It is represented by a marker chain which effects additional buoyancy when distorted out of its equilibrium position. When the compositional density contrast is greater than about 5%, the descending slab is deflected sidwards at the boundary and two-layer convection prevails. A resulting depression of the boundary in the range of 50-200 km should be detectable with seismic methods. Below 5% density difference the slab plunges several hundred kilometers into the lower mantle, and below 2% it will probably not stop before reaching the core-mantle boundary and extensive mixing would be expected. With a pure phase change a negative Clapeyron slope of about -6 MPa/K (~60 bar/K) is required to establish a type of ''leaky double-layer convection. A more moderate slope can aid a small compositional density difference to prevent slab penetration into the lower mantle. With the present uncertainties about the physical nature of the 650-km discontinuity, a variety of convection stypes appears possible on dynamical grounds.