Timestepping Schemes Based On Time Discontinuous Galerkin Methods

Thorsten Schindler 1 Vincent Acary 1
1 BIPOP - Modelling, Simulation, Control and Optimization of Non-Smooth Dynamical Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
Abstract : The contribution deals with timestepping schemes for nonsmooth dynamical systems. So far, these schemes are locally of order one, both in smooth and nonsmooth segments. This is inefficient for applications with few events like circuit breakers. To consistently improve the behavior during smooth episodes, the traditional schemes are being embedded in time discontinuous Galerkin methods. After establishing the correct mathematical setting, a Petrov-Galerkin distributional differential inclusion is outlined. The bouncing ball example illustrates the capabilities.
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Thorsten Schindler, Vincent Acary. Timestepping Schemes Based On Time Discontinuous Galerkin Methods. EUROMECH Colloqium 516. Nonsmooth contact and impact laws in mechanics, EUROMECH INRIA, Jul 2011, Grenoble, France. ⟨inria-00609890⟩

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