A Lagrangian Approach to Deriving Local-Energy-Preserving Numerical Schemes for the Euler-Lagrange Partial Differential Equations and an Application to the Nonreflecting Boundary Conditions for the Linear Wave Equation(Theory,<Special Topics>Activity Group "Scientific Computation and Numerical Analysis")

Abstract

We propose a Lagrangian approach to deriving local-energy-preserving finite difference schemes for the Euler-Lagrange partial differential equations regarding that, from Noether's theorem, the symmetry of time translation of Lagrangian yields the energy conservation law. We first observe that the local symmetry of time translation of Lagrangian derives the Euler-Lagrange equation and the energy conservation law, simultaneously. The new method is a combination of a discrete counter part of this statement and the discrete gradient method. As an application of the discrete local energy conservation law, we also discuss discretization of the nonreflecting boundary conditions for the linear wave equation.