论文标题
Yang-Mills方程的电荷连接混合方法
Charge-conserving hybrid methods for the Yang-Mills equations
论文作者
论文摘要
Yang-Mills方程将Maxwell的方程推广到非亚伯仪表基团，并且类似于电荷的数量是通过非线性时间演变在局部保守的。克里斯蒂安森（Christiansen）和温瑟（Winther）观察到，在非阿布尔案中，具有谎言代数值有限元差异形式的盖尔金方法似乎在全球范围内保存电荷，但在本地也没有保存，甚至不是在薄弱的意义上。我们引入了该方法的新杂交，根据混合变量给出了数值电荷的替代表达式，并表明局部，每个元素电荷保护法自动持有。
The Yang-Mills equations generalize Maxwell's equations to nonabelian gauge groups, and a quantity analogous to charge is locally conserved by the nonlinear time evolution. Christiansen and Winther observed that, in the nonabelian case, the Galerkin method with Lie algebra-valued finite element differential forms appears to conserve charge globally but not locally, not even in a weak sense. We introduce a new hybridization of this method, give an alternative expression for the numerical charge in terms of the hybrid variables, and show that a local, per-element charge conservation law automatically holds.
