On the enforcing energy conservation of time finite elements for discrete elasto-dynamics problems

In the context of the time-finite element method, algorithmic stresses, which enable the conservation of energy, are designed for temporal integrators derived from the midpoint and trapezoidal schemes. This is achieved through an appropriate modification of the standard midpoint and trapezoidal quadrature rules used for the numerical integration of time integrals. Either scalar scaling or vectorial adjustments can be employed for the modification, and well-designed simple tests allow to investigate the quality of these different strategies of energy-conserving enforcements. Numerical examples with semi-discrete elastodynamics problems are presented to show the superior stability of energy-conserving schemes. Copyright q 2006 John Wiley & Sons, Ltd.