Discretization of the Koch Snowflake Domain with Boundary and Interior Energies
Numerical Analysis
2020-05-29 v2 Numerical Analysis
Mathematical Physics
Analysis of PDEs
math.MP
Spectral Theory
Abstract
We study the discretization of a Dirichlet form on the Koch snowflake domain and its boundary with the property that both the interior and the boundary can support positive energy. We compute eigenvalues and eigenfunctions, and demonstrate the localization of high energy eigenfunctions on the boundary via a modification of an argument of Filoche and Mayboroda. H\"older continuity and uniform approximation of eigenfunctions are also discussed.
Keywords
Cite
@article{arxiv.2002.04680,
title = {Discretization of the Koch Snowflake Domain with Boundary and Interior Energies},
author = {Malcolm Gabbard and Carlos Lima and Gamal Mograby and Luke G. Rogers and Alexander Teplyaev},
journal= {arXiv preprint arXiv:2002.04680},
year = {2020}
}