DeepAI AI Chat
Log In Sign Up

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

by   Kthim Imeri, et al.
Simon Fraser University

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.


page 1

page 2

page 3

page 4


On the discretization of Laplace's equation with Neumann boundary conditions on polygonal domains

In the present paper we describe a class of algorithms for the solution ...

Regularity of the solution of the scalar Signorini problem in polygonal domains

The Signorini problem for the Laplace operator is considered in a genera...

The Projection Extension Method: A Spectrally Accurate Technique for Complex Domains

An essential ingredient of a spectral method is the choice of suitable b...

Numerical analysis for the Plateau problem by the method of fundamental solutions

Towards identifying the number of minimal surfaces sharing the same boun...

Nodal solutions of weighted indefinite problems

This paper analyzes the structure of the set of nodal solutions of a cla...

Power-SLIC: Diagram-based superpixel generation

Superpixel algorithms, which group pixels similar in color and other low...