SciCADE 2013
International Conference on Scientific Computation and Differential Equations
September 16-20, 2013, Valladolid (Spain)

Contributed Talk

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Lagrangian approach of the discrete gradient method based on finite element methods

T. Yaguchi

Abstract
In this talk, we propose a finite element framework of the Lagrangian approach of the discrete gradient method to deriving energy-preserving schemes for the Euler-Lagrange partial differential equations. Recently a framework that derives energy-preserving finite difference schemes for the Euler-Lagrange PDEs is proposed [1]. This approach is based on a combination of the symmetry of time translation of discrete Lagrangians and the discrete gradient method. In this talk, we show that the same combination is also workable on the finite element framework. Because our method is based on Lagrangian mechanics, this method can be said to be a Lagrangian counterpart of the energy-preserving method for Hamiltonian systems by Matsuo [2]. Some applications will be also provided.

Bibliography
[1] T. Yaguchi, Lagrangian approach to deriving energy-preserving numerical schemes for the Euler-Lagrange partial differential equations, M2AN, to appear.
[2] T. Matsuo, Dissipative/conservative Galerkin method using discrete partial derivative for nonlinear evolution equations, J. Comput. Appl. Math., 218 (2008), pp. 506-521.

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