A system and method for simulating a physical process in a simulation domain. Dividing the simulation domain into a first sub-domain and a gap region. The gap region defines a region of a specified width between a contact line of a droplet and the first sub-domain. Generating a mesh that represents the first sub-domain as a plurality of elements. The specification of each element includes an integer element number that represents an order of each element. The specified width of the gap region is on the order of half the width of an element in the first sub-domain adjoining the gap region divided by the integer element number. Using the finite element method and the mesh to calculate a state of the droplet at a first point in time. Using a plurality of evolution equations to calculate the state of the droplet at a second point in time.