In this paper we explore a robust approach to derive combined space-time discretization methods for two classes (parabolic and hyperbolic) of time-dependent PDEs. We use the popular FOSLS (first order systems least-squares) approach (cf., e.g., Cai et al. 1994 or Carey et al. 1995) treating time as an additional space variable and, in addition, we prescribe a space-time divergence equation as a constraint in order to maintain certain space-time mass conservation (following, e.g., Adler and Vassilevski 2014).
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机译：在本文中，我们探索了一种鲁棒的方法来推导针对时间相关的PDE的两类（抛物线和双曲线）的组合时空离散化方法。我们使用流行的FOSLS（一阶系统最小二乘）方法（例如，Cai等，1994或Carey等，1995）将时间视为附加的空间变量，此外，我们还规定了时空为了保持一定的时空质量守恒，将发散方程作为约束（例如，Adler and Vassilevski 2014）。
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