This article introduces an efficient numerical scheme for the solution of the Benjamin‐Bona‐Mahony equation. The scheme is fully implicit, and combines high‐order time stepping and a hybridizable discontinuous Galerkin method in space. Implicit time stepping allows for larger time steps, while remaining robust for long‐time simulations. It is shown that the scheme is energy stable, and conserves mass. Computational experiments demonstrate that the scheme is high‐order accurate, robust, and possesses good conservation properties.

中文翻译：

---

Benjamin-Bona-Mahony方程的高阶隐式可杂交不连续Galerkin方法

本文介绍了一种有效的数值方案，用于求解本杰明·波纳·马洪尼方程。该方案是完全隐式的，并且在空间中结合了高阶时间步长和可混合的不连续Galerkin方法。隐式时间步长允许更大的时间步长，同时对于长时间仿真仍然保持鲁棒性。结果表明，该方案能量稳定，节省了质量。计算实验表明，该方案具有高阶精度，鲁棒性和良好的保存性能。