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Journal of Computational Mathematics

Charge-conserving hybrid methods for the Yang–Mills equations
Yakov Berchenko-Kogan1; Ari Stern2
1 University of Hawaii
2 Washington University in St. Louis
The SMAI Journal of computational mathematics, Volume 7 (2021), pp. 97-119.

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.

Published online:
DOI: 10.5802/smai-jcm.73
Classification: 65M60
Keywords: finite element method, domain decomposition, conservation laws, charge conservation, Yang–Mills equations, Maxwell’s equations
Yakov Berchenko-Kogan 1; Ari Stern 2

1 University of Hawaii
2 Washington University in St. Louis
License: CC-BY-NC-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Yakov Berchenko-Kogan; Ari Stern. Charge-conserving hybrid methods for the Yang–Mills equations. The SMAI Journal of computational mathematics, Volume 7 (2021), pp. 97-119. doi : 10.5802/smai-jcm.73. https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.73/

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