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We present a solution to the conservation form (Eulerian form) of the quantumhydrodynamic equations which arise in chemical dynamics by implementing amixed/discontinuous Galerkin (MDG) finite element numerical scheme. We showthat this methodology is stable, showing good accuracy and a remarkable scaleinvariance in its solution space. In addition the MDG method is robust,adapting well to various initial-boundary value problems of particularsignificance in a range of physical and chemical applications. We further showexplicitly how to recover the Lagrangian frame (or pathline) solutions.

Quantum Hydrodynamics with Trajectories: The Nonlinear Conservation Form Mixed/Discontinuous Galerkin Method with Applications in Chemistry