  This paper proposes a decoupled numerical scheme of the time-dependent
Ginzburg--Landau equations under the temporal gauge. For the magnetic potential
and the order parameter, the discrete scheme adopts the second type Ned${\rm
\acute{e}}$lec element and the linear element for spatial discretization,
respectively; and a linearized backward Euler method and the first order
exponential time differencing method for time discretization, respectively. The
maximum bound principle (MBP) of the order parameter and the energy dissipation
law in the discrete sense are proved. The discrete energy stability and
MBP-preservation can guarantee the stability and validity of the numerical
simulations, and further facilitate the adoption of an adaptive time-stepping
strategy, which often plays an important role in long-time simulations of
vortex dynamics, especially when the applied magnetic field is strong. An
optimal error estimate of the proposed scheme is also given. Numerical examples
verify the theoretical results of the proposed scheme and demonstrate the
vortex motions of superconductors in an external magnetic field.
