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arXiv 2006.14082math.NAcs.NA
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wave equation的间断Galerkin:简化的先验误差分析

Discontinuous Galerkin for the wave equation: a simplified a priori error analysis

Neda Rezaei, Fardin Saedpanah

摘要:

基于$ \qq=0,1$次分段多项式的标准间断Galerkin方法,研究了二阶双曲型方程的时间半离散问题.本文的主要目的是提出一个简单而直接的先验误差分析的最佳顺序与最小的规则性要求的解决方案。还证明了时间一致范数误差估计。为此,对于一个更一般的问题,证明了离散问题的能量恒等式和稳定性估计。这些被用来证明最佳顺序的先验误差估计与最小的规则性要求的解决方案。结合经典的空间变量连续伽辽金有限元离散,形成全离散格式。给出了先验误差分析。数值实验验证了理论结果。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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