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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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.
Funding
The first author was supported by the German Research Foundation (DFG) in the Priority Programme SPP 1748 Reliable simulation techniques in solid mechanics under grant number BE6511/1-1. The second author is a member of the INdAM Research group GNCS and his research is partially supported by IMATI/CNR and by PRIN/MIUR. The first and third authors were supported by Mercator Research Center Ruhr (MERCUR) under grant Pr-2017-0017.
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Communicated by: Jon Wilkening
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Bertrand, F., Boffi, D. & G. de Diego, G. Convergence analysis of the scaled boundary finite element method for the Laplace equation. Adv Comput Math 47, 34 (2021). https://doi.org/10.1007/s10444-021-09852-z
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DOI: https://doi.org/10.1007/s10444-021-09852-z
Keywords
- Scaled boundary finite element method
- Error analysis
- Singular solutions
Mathematics Subject Classification (2010)
- 65N12
- 65N15
- 65N30
- 65N38