The maximal regularity property of discontinuous Galerkin methods for linear parabolic equations is used together with variational techniques to establish a priori and a posteriori error estimates of optimal order under optimal regularity assumptions. The analysis is set in the maximal regularity framework of UMD Banach spaces. Similar results were proved in an earlier work, based on the consistency analysis of Radau IIA methods. The present error analysis, which is based on variational techniques, is of independent interest, but the main motivation is that it extends to nonlinear parabolic equations; in contrast to the earlier work. Both autonomous and nonautonomous linear equations are considered.

翻译：本文利用线性抛物方程间断伽辽金方法的极大正则性，结合变分技术，在最优正则性假设下建立了最优阶的先验与后验误差估计。该分析基于UMD巴拿赫空间的极大正则性框架。早期研究基于Radau IIA方法的相容性分析已证明类似结果。本文采用的基于变分技术的误差分析方法具有独立意义，但其主要动机在于该方法可推广至非线性抛物方程——此点与早期工作形成对比。研究同时涵盖自治与非自治线性方程情形。