[1] The physics of steady driven magnetic reconnection at Earth's subsolar magnetopause is addressed. Three-dimensional, global magnetohydrodynamics (MHD) simulations of the magnetopause are compared with analytical solutions of the resistive MHD equations [Sonnerup and Priest, 1975] corresponding to magnetic field annihilation driven by an incompressible stagnation point flow. The simulations demonstrate that under steady southward interplanetary magnetic field conditions and when the plasma resistivity is spatially uniform, subsolar magnetopause reconnection occurs in long, thin Sweet-Parker current sheets via a flux pileup mechanism [Sonnerup and Priest, 1975;Priest and Forbes, 1986] (rather than in Petschek slow shock configurations). Magnetic energy piles up upstream of the magnetopause current sheet to accommodate the sub-Alfvénic solar wind inflow. The scaling of the pileup with Lundquist number, S, is consistent (approximately / S 1/4 ) with that predicted by the analytical, incompressible stagnation point flow solutions (though there are small corrections due to plasma compressibility in the simulations). Since there is a finite energy in the magnetosheath available to drive the magnetic pileup (and associated rapid magnetic reconnection), we expect the pileup to saturate and the reconnection rate to drop as the upstream plasma pressure drops to accommodate the pileup. Thus we expect the reconnection to stall, the rate vanishing in the limit S ! 1. We discuss the role of Hall electric fields in allowing the magnetic pileup to saturate before the reconnection begins to stall, permitting Alfvénic reconnection to occur in thin current sheets in the limit S ! 1.