  The aim of this work is to show an abstract framework to analyze the
numerical approximation by using a finite element method in space and a
Backward-Euler scheme in time of a family of degenerate parabolic problems. We
deduce sufficient conditions to ensure that the fully-discrete problem has a
unique solution and to prove quasi-optimal error estimates for the
approximation. Finally, we show a degenerate parabolic problem which arises
from electromagnetic applications and deduce its well-posedness and convergence
by using the developed abstract theory, including numerical tests to illustrate
the performance of the method and confirm the theoretical results. Keywords:
parabolic degenerate equations, parabolic-elliptic equations, finite element
method, backward Euler scheme, fully-discrete approximation, error estimates,
eddy current model.
