  We introduce a new approach for finite element simulations of the
time-dependent Ginzburg-Landau equations (TDGL) in a general curved polygon,
possibly with reentrant corners. Specifically, we reformulate the TDGL into an
equivalent system of equations by decomposing the magnetic potential to the sum
of its divergence-free and curl-free parts, respectively. Numerical simulations
of vortex dynamics show that, in a domain with reentrant corners, the new
approach is much more stable and accurate than the old approaches of solving
the TDGL directly (under either the temporal gauge or the Lorentz gauge); in a
convex domain, the new approach gives comparably accurate solutions as the old
approaches.
