Steklov Approximations of Harmonic Boundary Value Problems on Planar Regions
Analysis of PDEs
2016-09-26 v1
Abstract
Error estimates for approximations of harmonic functions on planar regions by subspaces spanned by the first harmonic Steklov eigenfunctions are found. They are based on the explicit representation of harmonic functions in terms of these harmonic Steklov eigenfunctions. When the region is a rectangle of aspect ratio h, some computational results regarding these approximations for problems with known explicit solutions are described.
Keywords
Cite
@article{arxiv.1609.07400,
title = {Steklov Approximations of Harmonic Boundary Value Problems on Planar Regions},
author = {Giles Auchmuty and Manki Cho},
journal= {arXiv preprint arXiv:1609.07400},
year = {2016}
}