Efficient algorithm and analysis for the Yang-Mills equations with temporal gauge

02/27/2023

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by   Ruiyang Li, et al.

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This paper discusses the finite element method for the Yang-Mills equations with temporal gauge. The new contributions reported in this paper are threefold: an efficient linearized strategy for the Lie bracket [A, A] is introduced, the novel implicit scheme in time for the Yang-Mills equations based on the above linearized strategy is presented, which preserves the conservation of its discrete energy and the error estimates for the semi-discrete scheme and the linearized scheme are proved. Finally, numerical test studies are then carried out to confirm the theoretical results.