Details
| Original language | English |
|---|---|
| Pages (from-to) | 147-175 |
| Number of pages | 29 |
| Journal | Computer Methods in Applied Mechanics and Engineering |
| Volume | 333 |
| Early online date | 31 Jan 2018 |
| Publication status | Published - 1 May 2018 |
Abstract
This article considers a unilateral contact problem for the wave equation. The problem is reduced to a variational inequality for the Dirichlet-to-Neumann operator for the wave equation on the boundary, which is solved in a saddle point formulation using boundary elements in the time domain. As a model problem, also a variational inequality for the single layer operator is considered. A priori estimates are obtained for Galerkin approximations both to the variational inequality and the mixed formulation in the case of a flat contact area, where the existence of solutions to the continuous problem is known. Numerical experiments demonstrate the performance of the proposed mixed method. They indicate the stability and convergence beyond flat geometries.
Keywords
- A priori error estimates, Boundary element method, Mixed method, Variational inequality, Wave equation
ASJC Scopus subject areas
- Engineering(all)
- Computational Mechanics
- Engineering(all)
- Mechanics of Materials
- Engineering(all)
- Mechanical Engineering
- Physics and Astronomy(all)
- General Physics and Astronomy
- Computer Science(all)
- Computer Science Applications
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Computer Methods in Applied Mechanics and Engineering, Vol. 333, 01.05.2018, p. 147-175.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Time domain boundary elements for dynamic contact problems
AU - Gimperlein, Heiko
AU - Meyer, Fabian
AU - Özdemir, Ceyhun
AU - Stephan, Ernst P.
N1 - Funding Information: H.G. acknowledges support by ERC Advanced Grant HARG 268105 and the EPSRC Impact Acceleration Account EP/K503915/1 . C.O. is supported by a scholarship of the Avicenna Foundation .
PY - 2018/5/1
Y1 - 2018/5/1
N2 - This article considers a unilateral contact problem for the wave equation. The problem is reduced to a variational inequality for the Dirichlet-to-Neumann operator for the wave equation on the boundary, which is solved in a saddle point formulation using boundary elements in the time domain. As a model problem, also a variational inequality for the single layer operator is considered. A priori estimates are obtained for Galerkin approximations both to the variational inequality and the mixed formulation in the case of a flat contact area, where the existence of solutions to the continuous problem is known. Numerical experiments demonstrate the performance of the proposed mixed method. They indicate the stability and convergence beyond flat geometries.
AB - This article considers a unilateral contact problem for the wave equation. The problem is reduced to a variational inequality for the Dirichlet-to-Neumann operator for the wave equation on the boundary, which is solved in a saddle point formulation using boundary elements in the time domain. As a model problem, also a variational inequality for the single layer operator is considered. A priori estimates are obtained for Galerkin approximations both to the variational inequality and the mixed formulation in the case of a flat contact area, where the existence of solutions to the continuous problem is known. Numerical experiments demonstrate the performance of the proposed mixed method. They indicate the stability and convergence beyond flat geometries.
KW - A priori error estimates
KW - Boundary element method
KW - Mixed method
KW - Variational inequality
KW - Wave equation
UR - http://www.scopus.com/inward/record.url?scp=85041462451&partnerID=8YFLogxK
U2 - 10.1016/j.cma.2018.01.025
DO - 10.1016/j.cma.2018.01.025
M3 - Article
AN - SCOPUS:85041462451
VL - 333
SP - 147
EP - 175
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
SN - 0045-7825
ER -