Abstract
In this paper, we study a non-linear hyperbolic system, occuring in the study of electromagnetic fields in the presence of superconductors. The constitutive relation between current density and the electric field is then highly non-linear. Based on a stability estimate in the dual space, we are able to prove the convergence of backward Euler's method toward the unique solution of the problem. This requires a compensated compactness argument (div-curl lemma) and the Minty–Browder procedure to pull weak convergence through a monotone non-linearity. Finally, we present the corresponding error estimates.
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