Charge-conserving hybrid methods for the Yang-Mills equations

Abstract: 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.