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.
Keywords: finite element method, domain decomposition, conservation laws, charge conservation, Yang–Mills equations, Maxwell’s equations
Yakov Berchenko-Kogan 1; Ari Stern 2
@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/} }
TY - JOUR AU - Yakov Berchenko-Kogan AU - Ari Stern TI - Charge-conserving hybrid methods for the Yang–Mills equations JO - The SMAI Journal of computational mathematics PY - 2021 SP - 97 EP - 119 VL - 7 PB - Société de Mathématiques Appliquées et Industrielles UR - https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.73/ DO - 10.5802/smai-jcm.73 LA - en ID - SMAI-JCM_2021__7__97_0 ER -
%0 Journal Article %A Yakov Berchenko-Kogan %A Ari Stern %T Charge-conserving hybrid methods for the Yang–Mills equations %J The SMAI Journal of computational mathematics %D 2021 %P 97-119 %V 7 %I Société de Mathématiques Appliquées et Industrielles %U https://smai-jcm.centre-mersenne.org/articles/10.5802/smai-jcm.73/ %R 10.5802/smai-jcm.73 %G en %F SMAI-JCM_2021__7__97_0
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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