| We discuss several techniques for proving compactness of sequences of approximate solutions to discretized evolution PDEs, with applications to convergence of finite volume discretizations of degenerate parabolic equations. While the well-known Aubin-Simon kind functional-analytic techniques were recently generalized to the discrete setting by Gallouët and Latché [12], here we discuss direct techniques for estimating the time translates of approximate solutions in the space $L^1$. One important result is the Kruzhkov time compactness lemma. Further, we describe a specific technique that benefits from the order-preservation for the underlying PDE, and recall the well-known methods based on nonlinear weak-* convergence and on the subsequent reduction of Young measures. |
