On Maximal Regularity Estimates for Discontinuous Galerkin Time-Discrete Methods
GEORGIOS D. AKRIVIS, Charalambos Makridakis · SIAM Journal on Numerical Analysis · 2022
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.