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.

翻译：Yang-Mills等式将Maxwell的方程式概括为非美籍测量组,类似收费的数量由非线性时间演变在当地保存。 Christiansen和Winther指出,在非美籍情况下,Galerkin方法与Lie algebra价值有限要素差异表似乎可以在全球范围节省费用,但并非在当地范围,甚至不是在一种薄弱的意义上。 我们引入了新混合方法,用混合变量来表示数字收费的替代表达方式,并表明本地的永久收费保护法自动有效。