Moving Dirichlet boundary conditions∗. (10th October 2014)

• Record Type: Journal Article
• Authors: Altmann, Robert
• Is Part Of: Mathematical modelling and numerical analysis. Volume 48:Part 6(2014)
• Page Start: 1859
• Page End: 1876
• Publication Date: 2014-10-10
• Subjects: Dirichlet boundary conditions, -- operator DAE, -- inf-sup condition, -- wave equation; Numerical analysis -- Periodicals; Mathematical models -- Periodicals; 510
• DOI: 10.1051/m2an/2014022
• Languages: English
• ISSNs: 0764-583X

Abstract

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.