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.
%0 Journal Article
%1 gimperlein2018domain
%A Gimperlein, Heiko
%A Meyer, Fabian
%A Özdemir, Ceyhun
%A Stephan, Ernst P.
%D 2018
%K ians imported
%P 147-175
%R 10.1016/j.cma.2018.01.025
%T Time domain boundary elements for dynamic contact problems
%V 333
%X 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.
@article{gimperlein2018domain,
abstract = {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.},
added-at = {2019-06-17T14:25:24.000+0200},
author = {Gimperlein, Heiko and Meyer, Fabian and Özdemir, Ceyhun and Stephan, Ernst P.},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/2673c2bbbc40927a5df32ae9af64bf440/britsteiner},
doi = {10.1016/j.cma.2018.01.025},
interhash = {1735ce47c3a94c54050c89574eb179c0},
intrahash = {673c2bbbc40927a5df32ae9af64bf440},
issn = {0045-7825},
journaltitle = {Computer Methods in Applied Mechanics and Engineering},
keywords = {ians imported},
language = {eng},
pages = {147-175},
timestamp = {2019-06-17T12:34:15.000+0200},
title = {Time domain boundary elements for dynamic contact problems},
volume = 333,
year = 2018
}