  The entropy-based moment method is a well-known discretization for the
velocity variable in kinetic equations which has many desirable theoretical
properties but is difficult to implement with high-order numerical methods. The
regularized entropy-based moment method was recently introduced to remove one
of the main challenges in the implementation of the entropy-based moment
method, namely the requirement of the realizability of the numerical solution.
In this work we use the method of relative entropy to prove the convergence of
the regularized method to the original method as the regularization parameter
goes to zero and give convergence rates. Our main assumptions are the
boundedness of the velocity domain and that the original moment solution is
Lipschitz continuous in space and bounded away from the boundary of
realizability. We provide results from numerical simulations showing that the
convergence rates we prove are optimal.
