We show that the second-order accurate generalized-$\alpha$ method on a uniform temporal mesh may be viewed as an implicit midpoint method on a shifted temporal mesh. With this insight, we demonstrate generalized-$\alpha$ time integration of a finite element spatial discretization of a conservation law system results in a fully-discrete method admitting discrete balance laws when (i) the time integration is second-order accurate, (ii) a uniform temporal mesh is employed, (iii) the spatial discretization is conservative, and (iv) conservation variables are discretized.
翻译:我们表明,关于统一时空网格的第二阶准确的通用-美元/正正负法方法可被视为一个转移时空网格的隐含中点方法。 我们通过这一洞察,可以证明,养护法系统空间分解的有限要素的通用-正负法时间整合导致一种完全分立法,在以下情况下可以接受分离平衡法:(一) 时间整合是第二阶准确的,(二) 采用统一的时空网格,(三) 空间分解是保守的,(四) 保护变量是分解的。