Moving Dirichlet boundary conditions
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 48 (2014) no. 6, p. 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 : https://doi.org/10.1051/m2an/2014022
Classification:  65J10,  65M60,  65M20
Keywords: 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 - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {EDP-Sciences},
volume = {48},
number = {6},
year = {2014},
pages = {1859-1876},
doi = {10.1051/m2an/2014022},
language = {en},
url = {http://www.numdam.org/item/M2AN_2014__48_6_1859_0}
}

Altmann, Robert. Moving Dirichlet boundary conditions. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 48 (2014) no. 6, pp. 1859-1876. doi : 10.1051/m2an/2014022. http://www.numdam.org/item/M2AN_2014__48_6_1859_0/

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