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.

翻译：本文讨论了时间规范下杨-米尔斯方程的有限元方法。本文报告的新贡献有三方面：针对李括号$[A, A]$引入了一种高效的线性化策略；基于上述线性化策略提出了杨-米尔斯方程的新型时间隐格式，该格式保持了离散能量的守恒性；证明了半离散格式和线性化格式的误差估计。最后，通过数值实验验证了理论结果。