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Moving Dirichlet boundary conditions∗

Published online by Cambridge University Press:  10 October 2014

Robert Altmann
Robert Altmann*
Affiliation:
Institut für Mathematik MA4-5, Technische Universität Berlin, Straße des 17. Juni 136, 10623 Berlin, Germany.. raltmann@math.tu-berlin.de
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Abstract

This paper develops a framework to include Dirichlet boundary conditions on a subset ofthe boundary which depends on time. In this model, the boundary conditions are weaklyenforced with the help of a Lagrange multiplier method. In order to avoid that the ansatzspace of the Lagrange multiplier depends on time, a bi-Lipschitz transformation, whichmaps a fixed interval onto the Dirichlet boundary, is introduced. An inf-sup condition aswell as existence results are presented for a class of second order initial-boundary valueproblems. For the semi-discretization in space, a finite element scheme is presented whichsatisfies a discrete stability condition. Because of the saddle point structure of theunderlying PDE, the resulting system is a DAE of index 3.

Keywords

Dirichlet boundary conditionsoperator DAEinf-sup conditionwave equation
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 48 , Issue 6 , November 2014 , pp. 1859 - 1876
Copyright
© EDP Sciences, SMAI 2014

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