Mathematics and System Engineering Faculty Publications

Document Type

Article

Publication Title

SMAI Journal of Computational Mathematics

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 [8] 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.

First Page

97

DOI

10.5802/smai-jcm.73

Publication Date

2021

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