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

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.