Convergence of the Rothe Method Applied to Operator DAEs Arising in Elastodynamics

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.