Multiscale Approximations for the Stationary Ginzburg-Landau Equation

Explore recent findings on discrete minimizers of the Ginzburg-Landau energy in finite element and multiscale spaces in this 44-minute lecture. Delve into the impact of the Ginzburg-Landau parameter $\kappa$ on superconductors, particularly its role in triggering vortex lattices. Learn about the importance of translating $\kappa$ into mesh resolution conditions through error estimates that explicitly consider both $\kappa$ and the spatial mesh width $h$. Examine analytical results for Lagrange finite elements, uncovering a previously unknown numerical pollution effect. Discover how multiscale techniques can enhance approximation properties in solving the stationary Ginzburg-Landau equation.