Approximation of minimizers of the Ginzburg–Landau energy in non-convex domains

In this work, we study the approximation of minimizers of the Ginzburg–Landau energy over non-convex polygonal and polyhedral domains. We discretize the order parameter with Lagrange finite elements and the vector potential with Nédélec elements. We show that under certain resolution conditions of the mesh sizes and the Ginzburg–Landau parameter, we obtain quasi-best approximation error bounds. In two dimensions, the order of convergence can be fully determined by the angle of the largest reentrant corner.