On the Stability of Mixed Finite-Element Formulations for High-Temperature Superconductors

In this article, we present and analyze the numerical stability of two coupled finite element formulations. The first one is $h$ - notation="LaTeX">$a$ -formulation well suited for modeling systems with superconductors ferromagnetic materials. second one, so-called notation="LaTeX">$t$ thin-shell approximation, applies thin superconducting domains. Both formulations involve unknown fields are mixed on coupling interfaces. Function spaces in must satisfy compatibility conditions to ensure problem reliability solution. We propose stable choices function using hierarchical basis functions demonstrate effectiveness approach simple 2D examples.