Energy Estimation in Numerical Scheme for Nonlinear Partial Differential Equations*

This paper discusses an energy estimation method in a numerical scheme, the Newmark-beta method for nonlinear partial differential equations in terms of the Stokes-Dirac structure. First, we show that the total energy of numerical systems can be detected by a boundary integration of energies distributed on a system domain in the Newmark-beta method for dynamical nonlinear numerical analyses. Next, we illustrate example applications of the estimation to flexible beams with large deformations.