MOVING DIRICHLET BOUNDARY CONDITIONS

作者：Altmann Robert^*

来源：ESAIM: Mathematical Modelling and Numerical Analysis , 2014, 48(6): 1859-1876.

DOI：10.1051/m2an/2014022

• Dirichlet boundary conditions
• operator DAE
• inf-sup condition
• wave equation

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.

• 出版日期2014-12