Comparison of Time Discretization Schemes to Simulate the Motion of an Inextensible Beam
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We compare three different time discretization schemes in combination with an augmented Lagrangian method to simulate the motion of an inextensible beam. The resulting saddle-point problem is solved with an Uzawa-Douglas-Rachford algorithm. The three schemes are tested on a benchmark with an analytical solution and on a more challenging application. We found that in order to obtain optimal convergence behavior in time, the stopping tolerance for the Uzawa-type algorithm should be balanced against the time step size.
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