# 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.

## Key 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.

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Source: https://tomesphere.com/paper/2302.13575