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The Finite Element Method for the Time-Dependent Gross--Pitaevskii Equation with Angular Momentum Rotation
We consider the time-dependent Gross--Pitaevskii equation describing the dynamics of rotating Bose--Einstein condensates and its discretization with the finite element method. We analyze a mass conserving Crank--Nicolson-type discretization and prove corresponding a priori error estimates with respect to the maximum norm in time and the $L^2$- and energy-norm in space. …