  We determine non-perturbatively a fixed-point (FP) action for fermions in the
two-dimensional U(1) gauge (Schwinger) model. Our parameterization for the
fermionic action has terms within a $7\times 7$ square on the lattice, using
compact link variables. With the Wilson fermion action as starting point we
determine the FP-action by iterating a block spin transformation (BST) with a
blocking factor of 2 in the background of non-compact gauge field
configurations sampled according to the (perfect) Gaussian measure. We simulate
the model at various values of $\beta$ and find excellent improvement for the
studied observables.
