Time integration error estimation for continuous Galerkin schemes

The purpose of this contribution is the time integration error estimation for continuous Galerkin schemes applied to the linear semi-discrete equation of motion. A special focus is on the effort for the error estimation for large finite element models. Error estimators for the global time integration error as well as for the local error in the last time interval are presented. The Galerkin formulation in time allows the application of the well-known duality based error estimation techniques for the estimation of the time integration error. The main effort of these error estimators is the computation of the dual solution. In order to diminish the computational effort for solving the dual problem the error estimation is carried out in a reduced modal basis. The relevant modes which have to remain in the basis can be determined via the initial conditions of the dual problem. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)