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

Fleurianne Herveline Bertrand; Daniele Boffi; Gonzalo G. de Diego

doi:10.1007/s10444-021-09852-z

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

Fleurianne Herveline Bertrand, Daniele Boffi, Gonzalo G. de Diego

Computer, Electrical and Mathematical Sciences and Engineering

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

The scaled boundary finite element method (SBFEM) is a relatively recent boundary element method that allows the approximation of solutions to partial differential equations (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 two numerical examples.

Original language	English (US)
Journal	Advances in Computational Mathematics
Volume	47
Issue number	3
DOIs	https://doi.org/10.1007/s10444-021-09852-z
State	Published - Apr 19 2021

Bibliographical note

KAUST Repository Item: Exported on 2021-05-04
Acknowledgements: We would like to thank the project partners Prof. Carolin Birk (Universität Duisburg-Essen, Germany) and Prof. Christian Meyer (TU Dortmund, Germany) as well as Professor Gerhard Starke for the fruitful discussions.

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1007/s10444-021-09852-z

https://repository.kaust.edu.sa/bitstream/10754/662991/3/Bertrand2021_Article_ConvergenceAnalysisOfTheScaled.pdf

Cite this

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title = "Convergence analysis of the scaled boundary finite element method for the Laplace equation",

abstract = "The scaled boundary finite element method (SBFEM) is a relatively recent boundary element method that allows the approximation of solutions to partial differential equations (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 two numerical examples.",

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N2 - The scaled boundary finite element method (SBFEM) is a relatively recent boundary element method that allows the approximation of solutions to partial differential equations (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 two numerical examples.

AB - The scaled boundary finite element method (SBFEM) is a relatively recent boundary element method that allows the approximation of solutions to partial differential equations (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 two numerical examples.

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

Abstract

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