1. Discretization of the Koch Snowflake Domain with Boundary and Interior Energies
- Author
-
Gabbard, Malcolm, Lima, Carlos, Mograby, Gamal, Rogers, Luke G., and Teplyaev, Alexander
- Subjects
Mathematics::Dynamical Systems ,Mathematics::Analysis of PDEs ,FOS: Physical sciences ,Numerical Analysis (math.NA) ,Mathematical Physics (math-ph) ,Mathematics::Spectral Theory ,28A80, 47A07, 46N40, 05C50, 60J45, 65F15, 65N22, 35Q40 ,Mathematics - Spectral Theory ,Mathematics - Analysis of PDEs ,FOS: Mathematics ,Mathematics - Numerical Analysis ,Spectral Theory (math.SP) ,Mathematical Physics ,Analysis of PDEs (math.AP) - 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.
- Published
- 2020