In this paper, we construct high order energy dissipative and conservative local discontinuous Galerkin methods for the Fornberg-Whitham type equations. We give the proofs for the dissipation and conservation for related conservative quantities. The corresponding error estimates are proved for the proposed schemes. The capability of our schemes for different types of solutions is shown via several numerical experiments. The dissipative schemes have good behavior for shock solutions, while for a long time approximation, the conservative schemes can reduce the shape error and the decay of amplitude significantly
翻译：在本文中, 我们为 Fornberg- Whitham 型方程式构建高顺序能量散发和保守的本地不连续Galerkin 方法。 我们为相关保守量的消散和保存提供证明。 相应的误差估计为拟议方案提供了证明。 我们不同类型解决方案计划的能力通过若干数字实验得到证明。 消散计划对休克解决方案具有良好行为, 而长期近似, 保守计划可以显著减少形状错误和振荡的衰变。
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