| Issue |
ESAIM: M2AN
Volume 48, Number 6, November-December 2014
|
|
|---|---|---|
| Page(s) | 1859 - 1876 | |
| DOI | https://doi.org/10.1051/m2an/2014022 | |
| Published online | 10 October 2014 | |
Moving Dirichlet boundary conditions∗
Institut für Mathematik MA4-5, Technische Universität Berlin, Straße des 17.
Juni 136, 10623 Berlin, Germany.
raltmann@math.tu-berlin.de
Received:
25
September
2013
Revised:
16
March
2014
This paper develops a framework to include Dirichlet boundary conditions on a subset of the boundary which depends on time. In this model, the boundary conditions are weakly enforced with the help of a Lagrange multiplier method. In order to avoid that the ansatz space of the Lagrange multiplier depends on time, a bi-Lipschitz transformation, which maps a fixed interval onto the Dirichlet boundary, is introduced. An inf-sup condition as well as existence results are presented for a class of second order initial-boundary value problems. For the semi-discretization in space, a finite element scheme is presented which satisfies a discrete stability condition. Because of the saddle point structure of the underlying PDE, the resulting system is a DAE of index 3.
Mathematics Subject Classification: 65J10 / 65M60 / 65M20
Key words: Dirichlet boundary conditions / operator DAE / inf-sup condition / wave equation
© EDP Sciences, SMAI 2014
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.