Preprint 20-2015

Convergence of the Rothe method applied to Operator DAEs arising in Elastodynamics

Author(s) : Robert Altmann

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 20-2015

MSC 2000

65J15 Equations with nonlinear operators

65M12 Stability and convergence of numerical methods

65M99 None of the above, but in this section

Abstract :
The dynamics of elastic media, constrained by Dirichlet boundary conditions, can be modeled as operator DAE of semi-explicit structure. These models include flexible multibody systems as well as applications with boundary control. In order to use adaptive methods in space, we analyse the properties of the Rothe method concerning stability and convergence for this kind of systems. For this, we consider a regularization of the operator DAE and prove the weak convergence of the implicit Euler scheme. Furthermore, we consider perturbations in the semi-discrete systems which correspond to additional errors such as spatial discretization errors.

Keywords : PDAE, operator DAE, regularization, evolution equations, elastodynamics, Rothe method, Euler method