Steklov eigenvalues for the Lam\'e operator in linear elasticity

Autor:	Domínguez, Sebastián
Rok vydání:	2020
Předmět:	Mathematics - Analysis of PDEs Mathematics - Numerical Analysis
Druh dokumentu:	Working Paper
DOI:	10.1016/j.cam.2021.113558
Popis:	In this paper we study Steklov eigenvalues for the Lam\'e operator which arise in the theory of linear elasticity. In this eigenproblem the spectral parameter appears in a Robin boundary condition, linking the traction and the displacement. To establish the existence of a countable spectrum for this problem, we present an extension of Korn's inequality. We also show that a proposed conforming Galerkin scheme provides convergent approximations to the true eigenvalues. A standard finite element method is used to conduct numerical experiments on 2D and 3D domains to support our theoretical findings. Comment: Submitted to JCAM
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2006.04308 Zobrazit plný text záznamu View this record from Arxiv