Fornberg-Whitham型方程的耗散守恒局部间断Galerkin方法
Dissipative and conservative local discontinuous Galerkin methods for the Fornberg-Whitham type equations
摘要：
本文构造了求解Fornberg-Whitham型方程的高阶能量耗散守恒局部间断Galerkin方法。给出了相关守恒量的耗散性和守恒性的证明。证明了相应的误差估计。通过几个数值实验表明，我们的计划为不同类型的解决方案的能力。耗散格式对激波解有较好的表现，而在长时间近似下，守恒格式能显著减小形状误差和振幅衰减
英文摘要：
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
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