Henry K. Harbury and Wolfgang Porod We present a method to solve the two-dimensional effective-mass Schrödinger equation for scattering states on open boundary domains. The boundary conditions are developed by partial wave expansion of the known far-field solution and by enforcing continuity of the complex wavefunction and its derivative across the domain periphery. The problem is formulated within the finite element method and the algorithm is used to solve for the scattering states of a two-dimensional electron gas with point scatterers. This technique may be used to study the local field effects within the vicinity of scattering defects in mesoscopic structures.