Preprint 24-2012

Index Reduction for Operator Differential-Algebraic Equations in Elastodynamics

Author(s) : Robert Altmann

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 24-2012

MSC 2000

65J15 Equations with nonlinear operators

65L80 Methods for differential-algebraic equations

65M60 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods

Abstract :
In space semi-discretized equations of elastodynamics with weakly enforced Dirichlet boundary conditions lead to differential algebraic equations (DAE) of index 3. We rewrite the continuous model as operator DAE and present an index reduction technique on operator level. This means that a semi-discretization leads directly to an index-1 system. We present existence results for the operator DAE with nonlinear damping term and show that the reformulated operator DAE is equivalent to the original equations of elastodynamics. Furthermore, we show that index reduction and semi-discretization in space commute.

Keywords : elastodynamics, operator DAE, index reduction, Dirichlet boundary conditions