  In this paper we formulate and analyze a space-time finite element method for
the numerical simulation of rotating electric machines where the finite element
mesh is fixed in space-time domain. Based on the Babu\v{s}ka--Ne\v{c}as theory
we prove unique solvability both for the continuous variational formulation and
for a standard Galerkin finite element discretization in the space-time domain.
This approach allows for an adaptive resolution of the solution both in space
and time, but it requires the solution of the overall system of algebraic
equations. While the use of parallel solution algorithms seems to be mandatory,
this also allows for a parallelization simultaneously in space and time. This
approach is used for the eddy current approximation of the Maxwell equations
which results in an elliptic-parabolic interface problem. Numerical results for
linear and nonlinear constitutive material relations confirm the applicability,
efficiency and accuracy of the proposed approach.
