An energy conservative discontinuous Galerkin scheme for a generalised third order KdV type equation is designed. Based on the conservation principle, we propose techniques that allow for the derivation of optimal a priori bounds for the linear KdV equation and a posteriori bounds for the linear and modified KdV equation. Extensive numerical experiments showcasing the good long time behaviour of the scheme are summarised which are in agreement with the analysis proposed.

中文翻译：

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离散哈密顿问题的保守伽辽金方法

设计了广义三阶KdV型方程的能量守恒不连续Galerkin格式。基于守恒原理，我们提出了允许推导线性 KdV 方程的最佳先验界限和线性和修正 KdV 方程的后验界限的技术。广泛的数值实验表明该方案的良好的长期行为被总结，这与所提出的分析是一致的。