  In this paper, we evaluate the electromagnetic and gravitational form factors
as well as the corresponding generalized parton distributions of the electron
using the Basis Light-front Quantization approach to QED. We compare our
results with those from light-front perturbation theory. We adopt a novel basis
with its scale depending on the constituents' longitudinal momentum fraction.
We show that this basis improves convergence of the form factors with
increasing basis dimension, compared to that calculated in the original basis
with fixed scale. These results both validate the BLFQ approach and provide
guidance for its efficient implementation in solving light-front Hamiltonian
mass eigenstates for more complex systems in QED and QCD.
