A Steklov-spectral approach for solutions of Dirichlet and Robin boundary value problems

Kthim Imeri; Nilima Nigam

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arXiv · 2209.08405

A Steklov-spectral approach for solutions of Dirichlet and Robin boundary value problems

Kthim Imeri·Nilima Nigam

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Abstract

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.

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BibTeX RIS

Kthim Imeri, Nilima Nigam. 2022-09-17. A Steklov-spectral approach for solutions of Dirichlet and Robin boundary value problems. https://arxiv.org/abs/2209.08405

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