A spectral method for solving nonhomogeneous Neumann boundary value problems on quadrilaterals
A spectral method for solving nonhomogeneous Neumann boundary value problems on quadrilaterals
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DOI：
10.1016/j.apnum.2020.05.025
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发表时间：
2020-11
影响因子：
2.8
通讯作者：
Tian-jun Wang;T. Sun
中科院分区：
文献类型：
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作者：
Tian-jun Wang;T. Sun
在本文中，我们开发了一种谱方法，本质上是在四边形上施加非齐次诺伊曼边界条件。建立了无理正交近似的结果，有利于该类偏微分方程的数值求解。作为应用，我们提供了两个模型问题的谱方案，并证明了它们的谱精度。描述了有效的数值实现。数值结果证明了所提出算法的高效率。
In this paper, we develop a spectral method with essential imposition of nonhomogeneous Neumann boundary condition on quadrilaterals. Results on irrational orthogonal approximation are established, which facilitate the numerical solutions of partial differential equations of the sort. As applications, we provide spectral schemes for two model problems, and prove their spectral accuracy. Efficient numerical implementations are described. Numerical results demonstrate high efficiency of the suggested algorithms.