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：本文利用线性抛物型方程间断伽辽金方法的极大正则性，结合变分技巧，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。该分析在UMD Banach空间的极大正则性框架下进行。先前已有工作基于Radau IIA方法的相容性分析证明了类似结果。本文基于变分技巧的误差分析具有独立价值，但其主要动机在于该方法可推广至非线性抛物型方程，此点与先前工作形成对比。文中同时考虑了自治与非自治线性方程。