Convergence analysis of the scaled boundary finite element method for the Laplace equation

Autor:	Bertrand, Fleurianne, Boffi, Daniele, de Diego, Gonzalo G.
Rok vydání:	2020
Předmět:	Mathematics - Numerical Analysis 65N12 65N15 (Primary) 65N38 (Secondary) G.1.2 G.1.8
Druh dokumentu:	Working Paper
Popis:	The scaled boundary finite element method (SBFEM) is a relatively recent boundary element method that allows the approximation of solutions to PDEs without the need of a fundamental solution. A theoretical framework for the convergence analysis of SBFEM is proposed here. This is achieved by defining a space of semi-discrete functions and constructing an interpolation operator onto this space. We prove error estimates for this interpolation operator and show that optimal convergence to the solution can be obtained in SBFEM. These theoretical results are backed by a numerical example. Comment: 15 pages, 3 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2005.02287 Zobrazit plný text záznamu View this record from Arxiv