第五阶Korteweg-de Vries型方程的最优收敛混合不连续伽辽金方法
Optimally convergent hybridizable discontinuous Galerkin method for fifth-order Korteweg-de Vries type equations
AI总结：
本文提出并分析了求解第五阶Korteweg-de Vries方程的首个混合不连续伽辽金方法，证明了该方法在适当选择稳定化函数时具有最优收敛性，通过数值实验验证了理论结果。
AI中文摘要：
我们开发并分析了求解第五阶Korteweg-de Vries（KdV）型方程的第一个混合不连续伽辽金（HDG）方法。我们证明了半离散方案在适当选择数值迹中的稳定化函数时是稳定的。对于线性化第五阶方程，我们证明了近似解及其四个空间导数以及时间导数都具有最优收敛率。数值实验验证了线性及非线性方程的最优收敛率，证实了我们的理论发现。
英文摘要：
We develop and analyze the first hybridizable discontinuous Galerkin (HDG) method for solving fifth-order Korteweg-de Vries (KdV) type equations. We show that the semi-discrete scheme is stable with proper choices of the stabilization functions in the numerical traces. For the linearized fifth-order equations, we prove that the approximations to the exact solution and its four spatial derivatives as well as its time derivative all have optimal convergence rates. The numerical experiments, demonstrating optimal convergence rates for both the linear and nonlinear equations, validate our theoretical findings.
