TY - JOUR
T1 - Convergence analysis of the scaled boundary finite element method for the Laplace equation
AU - Bertrand, Fleurianne Herveline
AU - Boffi, Daniele
AU - G. de Diego, Gonzalo
N1 - 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.
PY - 2021/4/19
Y1 - 2021/4/19
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.
UR - http://hdl.handle.net/10754/662991
UR - https://link.springer.com/10.1007/s10444-021-09852-z
UR - http://www.scopus.com/inward/record.url?scp=85104664417&partnerID=8YFLogxK
U2 - 10.1007/s10444-021-09852-z
DO - 10.1007/s10444-021-09852-z
M3 - Article
SN - 1572-9044
VL - 47
JO - Advances in Computational Mathematics
JF - Advances in Computational Mathematics
IS - 3
ER -