Convergence of the Rothe method applied to operator DAEs arising in elastodynamics. (English) Zbl 07174723
Summary: 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.
MSC:
| 65J08 | Numerical solutions to abstract evolution equations |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 65M99 | Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems |
Keywords:
PDAE; operator DAE; regularization; evolution equations; elastodynamics; Rothe method; Euler methodReferences:
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