This work extends the discrete compactness results of Walkington (SIAM J. Numer. Anal., 47(6):4680-4710, 2010) for high-order discontinuous Galerkin time discretizations of parabolic problems to more general function space settings. In particular, we show a discrete version of the Aubin-Lions-Simon lemma that holds for general Banach spaces $X$, $B$, and $Y$ satisfying $X \hookrightarrow B$ compactly and $B \hookrightarrow Y$ continuously. Our proofs rely on the properties of a time reconstruction operator and remove the need for quasi-uniform time partitions assumed in previous works.

翻译：本研究将Walkington (SIAM J. Numer. Anal., 47(6):4680-4710, 2010) 关于抛物问题高阶间断伽辽金时间离散化的离散紧致性结果推广至更一般的函数空间框架。特别地，我们证明了一个适用于一般Banach空间$X$、$B$和$Y$的Aubin-Lions-Simon引理的离散版本，其中要求$X \hookrightarrow B$为紧嵌入且$B \hookrightarrow Y$为连续嵌入。我们的证明依赖于时间重构算子的性质，并消除了先前工作中对拟一致时间剖分的假设。