We consider the discretization of a class of nonlinear parabolic equations by discontinuous Galerkin time-stepping methods and establish a priori as well as conditional a posteriori error estimates. Our approach is motivated by the error analysis in [9] for Runge-Kutta methods for nonlinear parabolic equations; in analogy to [9], the proofs are based on maximal regularity properties of discontinuous Galerkin methods for non-autonomous linear parabolic equations.

翻译：本文研究一类非线性抛物型方程的间断伽辽金时间步进离散方法，并建立先验及条件后验误差估计。我们的方法受到文献[9]中龙格-库塔方法处理非线性抛物型方程误差分析的启发；与[9]类似，证明基于非自治线性抛物型方程间断伽辽金方法的极大正则性性质。