Two-Grid Finite-Element Method for the Two-Dimensional Time-Dependent Schrödinger Equation (Advances in Applied Mathematics and Mechanics, 2013)
In this paper, we construct semi-discrete two-grid finite elementschemes and full-discrete two-grid finite element schemes for thetwo-dimensional time-dependent Schrödinger equation. Thesemi-discrete schemes are proved to be convergent with an optimalconvergence order and the full-discrete schemes, verified by anumerical example, work well and are more efficient than thestandard finite element method.