A new Galerkin spectral element method for fourth-order boundary value problems
A new Galerkin spectral element method for fourth-order boundary value problems
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DOI：
10.1080/00207160.2015.1011142
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发表时间：
2016-06
影响因子：
1.8
通讯作者：
T. Sun;Lijun Yi
中科院分区：
文献类型：
--
作者：
T. Sun;Lijun Yi
本文针对一维四阶边值问题，提出了一种新的伽辽金谱元方法。首先在一维上引入了一些拟正交近似，并建立了一系列关于这些近似的结果，为谱元法的研究提供了有力的工具。将这些结果应用于四阶边值问题，建立了伽辽金谱元法的锐界和误差界。详细实现了该高效算法。数值结果表明，该方法具有较高的精度，较好地验证了理论分析。
In this paper, we propose a new Galerkin spectral element method for one-dimensional fourth-order boundary value problems. We first introduce some quasi-orthogonal approximations in one dimension, and establish a series of results on these approximations, which serve as powerful tools in the spectral element method. By applying these results to the fourth-order boundary value problems, we establish sharp and error bounds of the Galerkin spectral element method. The efficient algorithm is implemented in detail. Numerical results demonstrate its high accuracy, and confirm the theoretical analysis well.