Yang-Mills方程的电荷守恒混合方法
Charge-conserving hybrid methods for the Yang-Mills equations
摘要：
Yang-Mills方程将Maxwell方程推广到非交换规范群，并通过非线性时间演化使一个类似于电荷的量局部守恒。Christiansen和Winther观察到，在非交换的情况下，具有李代数值有限元微分形式的Galerkin方法似乎全局守恒，但不是局部守恒，甚至在弱意义上也不是。我们介绍了一种新的杂交这种方法，给出了另一种表达式的混合变量的数值收费，并显示，本地，每元素的收费守恒律自动举行。
英文摘要：
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.
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