论文标题
Dirichlet和Robin边界价值问题解决方案的Steklov-Spectral方法
A Steklov-spectral approach for solutions of Dirichlet and Robin boundary value problems
论文作者
论文摘要
在本文中，我们重新审视了Auchmuty开创的一种方法，以近似Laplace-Robin边界价值问题的解决方案。与其他光谱方法相反，我们证明了这种方法对大量非感情领域的功效。 我们建立一个光谱近似定理，显示了用于平滑域和平滑边界数据的steklov本特征函数数量的指数快速数值评估。对于非平滑域或非平滑边界数据，观察到多项式快速数值评估。另外，我们还证明了steklov特征函数的规律性的新结果，具体取决于域边界的规律性。 我们描述了三种计算steklov本征函数的数值方法。
In this paper we revisit an approach pioneered by Auchmuty to approximate solutions of the Laplace- Robin boundary value problem. We demonstrate the efficacy of this approach on a large class of non-tensorial domains, in contrast with other spectral approaches for such problems. We establish a spectral approximation theorem showing an exponential fast numerical evaluation with regards to the number of Steklov eigenfunctions used, for smooth domains and smooth boundary data. A polynomial fast numerical evaluation is observed for either non-smooth domains or non-smooth boundary data. We additionally prove a new result on the regularity of the Steklov eigenfunctions, depending on the regularity of the domain boundary. We describe three numerical methods to compute Steklov eigenfunctions.
