Geodesic
Moving Dirichlet boundary conditions
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 48 (2014) no. 6, pp. 1859-1876

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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.

DOI : 10.1051/m2an/2014022
Classification : 65J10, 65M60, 65M20
Keywords: Dirichlet boundary conditions, operator DAE, inf-sup condition, wave equation 
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     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://geodesic.mathdoc.fr/articles/10.1051/m2an/2014022/}
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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

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