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

Fleurianne Bertrand, Daniele Boffi, Gonzalo G. de Diego

Research output: Working paper

14 Downloads (Pure)

Abstract

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.
Original languageEnglish
PublisherArXiv
Number of pages13
Publication statusPublished - 2020
Externally publishedYes

Keywords

  • math.NA
  • cs.NA
  • 65N12
  • G.1.2
  • G.1.8
  • 65N15 (Primary)
  • 65N38 (Secondary)

Fingerprint

Dive into the research topics of 'Convergence analysis of the scaled boundary finite element method for the Laplace equation'. Together they form a unique fingerprint.

Cite this