Moving Dirichlet boundary conditions

Robert Altmann

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2014)

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

Abstract

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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.

How to cite

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Altmann, 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 -

References

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