direkt zum Inhalt springen

direkt zum Hauptnavigationsmenü

Sie sind hier

TU Berlin

Inhalt des Dokuments

Preprint 12-2013

Moving Dirichlet Boundary Conditions

Source file is available as :   Portable Document Format (PDF)

Author(s) : Robert Altmann

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 12-2013

MSC 2000

65J10 Equations with linear operators
65M60 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
65M20 Method of lines

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.

Keywords : Dirichlet boundary conditions, operator DAE, inf-sup condition, wave equation

Zusatzinformationen / Extras


Schnellnavigation zur Seite über Nummerneingabe