A Petrov–Galerkin spectral method for fourth‐order problems
A Petrov–Galerkin spectral method for fourth‐order problems
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DOI：
10.1002/mma.2973
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发表时间：
2014-10
影响因子：
2.9
通讯作者：
T. Sun;Lijun Yi
中科院分区：
文献类型：
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作者：
T. Sun;Lijun Yi
本文考虑了在非齐次Dirichlet边界条件下矩形区域上的四阶椭圆问题的Petrov-Galerkin谱方法。我们得到了一维和二维正交近似的一些尖锐结果，这些结果在高阶问题的数值解中起着重要的作用。通过将这些结果应用于一个四阶问题，我们建立了Petrov-Galerkin谱方法的H2误差和L2误差界。数值实验结果表明，该方法具有较高的精度，与理论分析结果吻合较好。版权所有©2013 John Wiley & Sons， Ltd
In this paper, we consider the Petrov–Galerkin spectral method for fourth‐order elliptic problems on rectangular domains subject to non‐homogeneous Dirichlet boundary conditions. We derive some sharp results on the orthogonal approximations in one and two dimensions, which play important roles in numerical solutions of higher‐order problems. By applying these results to a fourth‐order problem, we establish the H2‐error and L2‐error bounds of the Petrov–Galerkin spectral method. Numerical experiments are provided to illustrate the high accuracy of the proposed method and coincide well with the theoretical analysis. Copyright © 2013 John Wiley & Sons, Ltd.