In this paper, we construct semi-discrete two-grid finite element
schemes and full-discrete two-grid finite element schemes for the
two-dimensional time-dependent Schrodinger equation. The
semi-discrete schemes are proved to be convergent with an optimal
convergence order and the full-discrete schemes, verified by a
numerical example, work well and are more efficient than the
standard finite element method.
Schrodinger equation two-grid method finite element method