A front-tracking algorithm for interfacial flows is reviewed. The interface is described by a set of closed lines. Fixed markers are set at the crossing points of these lines, while auxiliary markers are defined at the intersection points with the grid cell faces and inside each computational cell. These auxiliary markers are added and removed dynamically by a local area conservation algorithm. A Navier-Stokes solver that includes this front-tracking algorithm has been developed for 2D incompressible two-phase flows based on the finite element method. A variational formulation of the surface tension term, which removes the singularity of the capillary force, is proposed. Spurious currents are greatly reduced and oscillating drop dynamics is accurately reproduced.