Stability of H-A and T-A Finite Element Formulations
Julien Dular  1@  , Harutyunyane Mané  2  , Sebastian Schöps  2  , Benoit Vanderheyden  3@  , Christophe Geuzaine  1@  
1 : University of Liège
Liège -  Belgium
2 : Technical University of Darmstadt
3 : Department of Electrical Engineering and Computer Science
Department of Electrical Engineering and Computer Science, University of Liège, Liège, 4000, Belgium -  Belgium

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

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