Details
| Original language | English |
|---|---|
| Pages (from-to) | 35-101 |
| Number of pages | 67 |
| Journal | Numerische Mathematik |
| Volume | 154 |
| Issue number | 1-2 |
| Early online date | 22 May 2023 |
| Publication status | Published - Jun 2023 |
Abstract
The solution to the elastodynamic equation in the exterior of a polyhedral domain or a screen exhibits singular behavior from the corners and edges. The detailed expansion of the singularities implies quasi-optimal estimates for piecewise polynomial approximations of the Dirichlet trace of the solution and the traction. The results are applied to hp and graded versions of the time domain boundary element method for the weakly singular and the hypersingular integral equations. Numerical examples confirm the theoretical results for the Dirichlet and Neumann problems for screens and for poly- gonal domains in 2d. They exhibit the expected quasi-optimal convergence rates and the singular behavior of the solutions.
ASJC Scopus subject areas
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
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In: Numerische Mathematik, Vol. 154, No. 1-2, 06.2023, p. 35-101.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Higher-order time domain boundary elements for elastodynamics
T2 - graded meshes and hp versions
AU - Aimi, Alessandra
AU - Di Credico, Giulia
AU - Gimperlein, Heiko
AU - Stephan, Ernst P.
N1 - Funding Information: This work has been partially supported by the University of Parma with the project Fil2020 - Action A1 “Time-domain Energetic BEM for elastodynamic problems, with advanced applications”. This research was further supported through the “Oberwolfach Research Fellows” program in 2020.
PY - 2023/6
Y1 - 2023/6
N2 - The solution to the elastodynamic equation in the exterior of a polyhedral domain or a screen exhibits singular behavior from the corners and edges. The detailed expansion of the singularities implies quasi-optimal estimates for piecewise polynomial approximations of the Dirichlet trace of the solution and the traction. The results are applied to hp and graded versions of the time domain boundary element method for the weakly singular and the hypersingular integral equations. Numerical examples confirm the theoretical results for the Dirichlet and Neumann problems for screens and for poly- gonal domains in 2d. They exhibit the expected quasi-optimal convergence rates and the singular behavior of the solutions.
AB - The solution to the elastodynamic equation in the exterior of a polyhedral domain or a screen exhibits singular behavior from the corners and edges. The detailed expansion of the singularities implies quasi-optimal estimates for piecewise polynomial approximations of the Dirichlet trace of the solution and the traction. The results are applied to hp and graded versions of the time domain boundary element method for the weakly singular and the hypersingular integral equations. Numerical examples confirm the theoretical results for the Dirichlet and Neumann problems for screens and for poly- gonal domains in 2d. They exhibit the expected quasi-optimal convergence rates and the singular behavior of the solutions.
UR - http://www.scopus.com/inward/record.url?scp=85160106912&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2305.00772
DO - 10.48550/arXiv.2305.00772
M3 - Article
AN - SCOPUS:85160106912
VL - 154
SP - 35
EP - 101
JO - Numerische Mathematik
JF - Numerische Mathematik
SN - 0029-599X
IS - 1-2
ER -