A posteriori error estimates for Radau IIA methods via maximal parabolic regularity

We consider the discretization of differential equations satisfying the maximal parabolic Lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^p$$\end{document}-regularity property in Banach spaces by Radau IIA methods. We establish a posteriori error estimators via the maximal parabolic regularity of the differential equation. To complete the picture, we utilize the maximal parabolic regularity of the numerical methods to prove that the estimators are of optimal order.