Charge-conserving hybrid methods for the Yang–Mills equations
Berchenko-Kogan, Yakov1 ; Stern, Ari2
1 University of Hawaii
2 Washington University in St. Louis
The SMAI Journal of computational mathematics, Tome 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.

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

1 University of Hawaii
2 Washington University in St. Louis 
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Berchenko-Kogan, Yakov; Stern, Ari. Charge-conserving hybrid methods for the Yang–Mills equations. The SMAI Journal of computational mathematics, Tome 7 (2021), pp. 97-119. doi : 10.5802/smai-jcm.73. http://www.numdam.org/articles/10.5802/smai-jcm.73/

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