论文标题
对角隐式runge-kutta方案：离散的能量平衡法和紧凑特性
Diagonally implicit Runge-Kutta schemes: Discrete energy-balance laws and compactness properties
论文作者
论文摘要
当应用于适合Gelfand-Triple框架的抽象进化问题时，我们研究对角线隐式runge-kutta（Dirk）方案。我们介绍了非常适合这种设置的新型稳定概念，并提供了简单，必要和充分的条件，以验证Dirk方案在我们的意义上和Bochner型规范中是稳定的。我们使用几种流行的DIRK计划来说明满足所需结构稳定性属性和不符合的情况的情况。此外，在问题上，我们可以保证离散解决方案家族在时间离散化方面的紧凑性。
We study diagonally implicit Runge-Kutta (DIRK) schemes when applied to abstract evolution problems that fit into the Gelfand-triple framework. We introduce novel stability notions that are well-suited to this setting and provide simple, necessary and sufficient, conditions to verify that a DIRK scheme is stable in our sense and in Bochner-type norms. We use several popular DIRK schemes in order to illustrate cases that satisfy the required structural stability properties and cases that do not. In addition, under some mild structural conditions on the problem we can guarantee compactness of families of discrete solutions with respect to time discretization.
