On the enforcing energy conservation of time-finite elements for particle systems

In the framework of the time-finite element method, energy-conserving temporal integrators are developed through the design of non-standard quadrature. The latter can be achieved by a global enforcement of the force field issued from the standard quadrature. This might, however, lead to an undesirable coupling of all degrees of freedom. A local enforcement is suggested to enhance the enforcement of energy conservation through a tailored modification to each component of acting forces. Representative examples for non-linear particle systems are presented in order to examine the quality of various approaches in the enforcement of energy conservation. Copyright 2006 John Wiley & Sons, Ltd