高阶偏微分方程局部间断Galerkin方法的最优误差估计

摘要

本文针对含三阶和四阶空间导数的高阶偏微分方程,得到了基于广义交替数值通量局部间断Galerkin方法的最优L2-模误差估计.主要技术是基于有关辅助变量的能量方程和最新提出的整体Gauss-Radau投影.数值实验验证了理论结果.%We study the local discontinuous Galerkin (LDG) method based on the generalized alternating numerical fluxes for the high order partial differential equation containing the third order or fourth order spatial derivative terms.Optimal L2-norm error estimates are obtained for the corresponding semi-discrete LDG method.The main technique is to derive the energy equation for various auxiliary variables and to use the newly developed generalized Gauss-Radau projection.Numerical experiments are given to verify the sharpness of the theoretical results.