A Steklov-spectral approach for solutions of Dirichlet and Robin boundary value problems
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.
Cite
@article{arxiv.2209.08405,
title = {A Steklov-spectral approach for solutions of Dirichlet and Robin boundary value problems},
author = {Kthim Imeri and Nilima Nigam},
journal= {arXiv preprint arXiv:2209.08405},
year = {2022}
}