Abstract
The dynamics of elastic media, constrained by Dirichlet boundary conditions, can be modeled as an 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 analyze the properties of the Rothe method concerning stability and convergence for this kind of systems. 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.
Funding statement: The work of the author was supported by the ERC Advanced Grant “Modeling, Simulation and Control of Multi-Physics Systems” MODSIMCONMP and the Berlin Mathematical School BMS.
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