Author(s) :
Robert Altmann
Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 242012
MSC 2000
 65J15 Equations with nonlinear operators

65L80 Methods for differentialalgebraic equations

65M60 Finite elements, RayleighRitz and Galerkin methods, finite methods
Abstract :
In space semidiscretized 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 semidiscretization leads directly to an index1 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 semidiscretization in space commute.
Keywords :
elastodynamics, operator DAE, index reduction, Dirichlet boundary conditions