ON MAXIMAL REGULARITY ESTIMATES FOR DISCONTINUOUS GALERKIN TIME-DISCRETE METHODS

We consider the discretization of differential equations satisfying the maximal parabolic L-P-regularity property in Banach spaces by discontinuous Galerkin methods. We use the maximal regularity framework to establish that the discontinuous Galerkin methods preserve the maximal L-P-regularity, satisfy corresponding a posteriori error estimates, and the estimators are of optimal asymptotic order of convergence. In our proofs, we use a suitable interpretation of the discontinuous Galerkin methods as modified Radau IIA methods.