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

TL;DR

This paper introduces an efficient linearized strategy and a novel implicit time scheme for solving the Yang-Mills equations with temporal gauge, ensuring energy conservation and providing error estimates, validated through numerical tests.

Contribution

It presents a new linearized approach and an implicit scheme for Yang-Mills equations that improve computational efficiency and theoretical understanding.

Findings

The linearized strategy effectively simplifies the Lie bracket computation.

The implicit scheme conserves discrete energy.

Numerical tests confirm the theoretical error estimates.

Abstract

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.