基于特征相关网格的不连续Galerkin法

The Discontinuous GaIerkin Method on the Characteristic ReIated Mesh

不连续Galerkin法是求解一阶双曲方程的有效方法,然而其解的逼近能否达到丰满阶,(特别是在解不连续的情况下),逼近解的收敛性能否得到保证是理论上尚未解决的问题。针对上述问题,本文提出了特征相关网格,并将其用于不连续的Galerkin法。理论分析和计算结果表明,上述方法可将已有的解的L_2误差估计提高半阶。

The discontinuous Galerkin method is a valid algorithm for the hyperbolic equation of the first order. But there are some problems to be solved, such as the optimal error estimate and the convergence for the discontinuous solution. In this paper, a characteristic related mesh is constructed, and is used for the discontinuous Galerkin method. It is shown by the theoretic analysis and calculation results that the optimal error estimate can be achieved, and the L_2 error can be O(h^(1/2)) accuracy even though the exact solution has some gaps.