Please use this identifier to cite or link to this item: http://dx.doi.org/10.14279/depositonce-14557
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Main Title: Moving Dirichlet Boundary Conditions
Author(s): Altmann, Robert
Type: Research Paper
URI: https://depositonce.tu-berlin.de/handle/11303/15784
http://dx.doi.org/10.14279/depositonce-14557
License: http://rightsstatements.org/vocab/InC/1.0/
Abstract: 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.
Subject(s): Dirichlet boundary conditions
operator DAE
inf-sup condition
wave equation
Issue Date: 24-Sep-2013
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 65J10 Equations with linear operators
65M60 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
65M20 Method of lines
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2013, 12
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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