|Date:||Thu, April 12, 2012|
|Place:||Research I Seminar Room|
Abstract: Variational Integrators, a family of symplectic methods, have become increasingly popular due to their versatility and simplicity of construction. For the construction of variational integration methods, only an approximation of the underlying Lagrangian function is required. Once the approximation is chosen, the discrete dynamic equations can be derived systematically. The error order analysis of variational integrators relies on the relationship between the order of accuracy of an integrator with the order of approximation of the exact discrete Lagrangian. The latter is not apparent due to the nontrivial coupling between quadrature formulas and polynomial interpolation, which are used in many standard approaches. I will talk about new classes of integrators which incorporate existing techniques from approximation theory, numerical quadrature, and one-step methods into the variational integration framework, and allow for straightforward order estimates.