  Theoretical uncertainties in the predictions of inner fission barrier heights
in superheavy elements have been investigated in a systematic way for a set of
state-of-the-art covariant energy density functionals which represent major
classes of the functionals used in covariant density functional theory. They
differ in basic model assumptions and fitting protocols. Both systematic and
statistical uncertainties have been quantified where the former turn out to be
larger. Systematic uncertainties are substantial in superheavy elements and
their behavior as a function of proton and neutron numbers contains a large
random component. The benchmarking of the functionals to the experimental data
on fission barriers in the actinides allows to reduce the systematic
theoretical uncertainties for the inner fission barriers of unknown superheavy
elements. However, even then they on average increase on moving away from the
region where benchmarking has been performed. In addition, a comparison with
the results of non-relativistic approaches is performed in order to define full
systematic theoretical uncertainties over the state-of-the-art models. Even for
the models benchmarked in the actinides, the difference in the inner fission
barrier height of some superheavy elements reaches $5-6$ MeV. This uncertainty
in the fission barrier heights will translate into huge (many tens of the
orders of magnitude) uncertainties in the spontaneous fission half-lives.
