Mass preserving discontinuous Galerkin methods for Schrdinger equations
We construct, analyze and numerically validate a class of mass preserving, direct discontinuous Galerkin (DDG) schemes for Schrdinger equations subject to both linear and nonlinear potentials. Up to round-off error, these schemes preserve the discrete version of the mass of the continuous solution. For time discretization, we use the CrankNicolson for linear Schrdinger equations, and the Strang splitting for nonlinear Schrdinger equations, so that numerical mass is still preserved at each time step. The DDG method when applied to linear Schrdinger equations is shown to have the optimal (k+1 k + 1 )th order of accuracy for polynomial elements of degree k. The numerical tests demonstrate both accuracy and capacity of these methods.
schrdinger equation ddg method numerical flux mass conservation strang splitting method