Charge-conserving hybrid methods for the Yang–Mills equations
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: https://doi.org/10.5802/smai-jcm.73
Classification: 65M60
Keywords: finite element method, domain decomposition, conservation laws, charge conservation, Yang–Mills equations, Maxwell’s equations
@article{SMAI-JCM_2021__7__97_0,
     author = {Yakov Berchenko-Kogan and Ari Stern},
     title = {Charge-conserving hybrid methods for the {Yang{\textendash}Mills} equations},
     journal = {The SMAI journal of computational mathematics},
     pages = {97--119},
     publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles},
     volume = {7},
     year = {2021},
     doi = {10.5802/smai-jcm.73},
     language = {en},
     url = {https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.73/}
}
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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