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.
Mots clés : Dirichlet boundary conditions, operator DAE, inf-sup condition, wave equation
@article{M2AN_2014__48_6_1859_0, author = {Altmann, Robert}, title = {Moving {Dirichlet} boundary conditions}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis }, pages = {1859--1876}, publisher = {EDP-Sciences}, volume = {48}, number = {6}, year = {2014}, doi = {10.1051/m2an/2014022}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an/2014022/} }
TY - JOUR AU - Altmann, Robert TI - Moving Dirichlet boundary conditions JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2014 SP - 1859 EP - 1876 VL - 48 IS - 6 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2014022/ DO - 10.1051/m2an/2014022 LA - en ID - M2AN_2014__48_6_1859_0 ER -
Altmann, Robert. Moving Dirichlet boundary conditions. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 48 (2014) no. 6, pp. 1859-1876. doi : 10.1051/m2an/2014022. http://www.numdam.org/articles/10.1051/m2an/2014022/
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