论文标题
波动方程的不连续盖尔金：简化的先验误差分析
Discontinuous Galerkin for the wave equation: a simplified a priori error analysis
论文作者
论文摘要
对于二阶双曲线方程的时间半差异，考虑了基于度量$ \ qq = 0,1 $的分段多项式的标准不连续的Galerkin方法。本文的主要目的是简单明了地对最佳顺序的先验错误分析，对解决方案的规律要求最小。还证明了统一的时间错误估计。为此，证明了离散问题的能量身份和稳定性估计是一个更普遍的问题。这些用于证明最佳的先验误差估计值，而解决方案的规律性最小。使用在空间变量中与经典连续的Galerkin有限元离散化的组合，以制定全盘式方案。提出了先验错误分析。进行数值实验以验证理论结果。
Standard discontinuous Galerkin methods, based on piecewise polynomials of degree $ \qq=0,1$, are considered for temporal semi-discretization for second order hyperbolic equations. The main goal of this paper is to present a simple and straightforward a priori error analysis of optimal order with minimal regularity requirement on the solution. Uniform norm in time error estimates are also proved. To this end, energy identities and stability estimates of bthe discrete problem are proved for a slightly more general problem. These are used to prove optimal order a priori error estimates with minimal regularity requirement on the solution. The combination with the classic continuous Galerkin finite element discretization in space variable is used, to formulate a full-discrete scheme. The a priori error analysis is presented. Numerical experiments are performed to verify the theoretical results.
