# Moving Dirichlet boundary conditions

- Volume: 48, Issue: 6, page 1859-1876
- ISSN: 0764-583X

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topAltmann, Robert. "Moving Dirichlet boundary conditions." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 48.6 (2014): 1859-1876. <http://eudml.org/doc/273241>.

@article{Altmann2014,

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.},

author = {Altmann, Robert},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {Dirichlet boundary conditions; operator DAE; inf-sup condition; wave equation; elastodynamics; moving Dirichlet boundary condition; weak constraint; saddle point formulation; finite elements; Lagrange multiplier method},

language = {eng},

number = {6},

pages = {1859-1876},

publisher = {EDP-Sciences},

title = {Moving Dirichlet boundary conditions},

url = {http://eudml.org/doc/273241},

volume = {48},

year = {2014},

}

TY - JOUR

AU - Altmann, Robert

TI - Moving Dirichlet boundary conditions

JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

PY - 2014

PB - EDP-Sciences

VL - 48

IS - 6

SP - 1859

EP - 1876

AB - 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.

LA - eng

KW - Dirichlet boundary conditions; operator DAE; inf-sup condition; wave equation; elastodynamics; moving Dirichlet boundary condition; weak constraint; saddle point formulation; finite elements; Lagrange multiplier method

UR - http://eudml.org/doc/273241

ER -

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