# Lagrangian approach to deriving energy-preserving numerical schemes for the Euler–Lagrange partial differential equations

- Volume: 47, Issue: 5, page 1493-1513
- ISSN: 0764-583X

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topYaguchi, Takaharu. "Lagrangian approach to deriving energy-preserving numerical schemes for the Euler–Lagrange partial differential equations." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 47.5 (2013): 1493-1513. <http://eudml.org/doc/273182>.

@article{Yaguchi2013,

abstract = {We propose a Lagrangian approach to deriving energy-preserving finite difference schemes for the Euler–Lagrange partial differential equations. Noether’s theorem states that the symmetry of time translation of Lagrangians yields the energy conservation law. We introduce a unique viewpoint on this theorem: “the symmetry of time translation of Lagrangians derives the Euler–Lagrange equation and the energy conservation law, simultaneously.” The proposed method is a combination of a discrete counter part of this statement and the discrete gradient method. It is also shown that the symmetry of space translation derives momentum-preserving schemes. Finally, we discuss the existence of discrete local conservation laws.},

author = {Yaguchi, Takaharu},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {discrete gradient method; energy-preserving integrator; finite difference method; lagrangian mechanics; Lagrangian mechanics; Hamilton-Jacobi equation; conservation law},

language = {eng},

number = {5},

pages = {1493-1513},

publisher = {EDP-Sciences},

title = {Lagrangian approach to deriving energy-preserving numerical schemes for the Euler–Lagrange partial differential equations},

url = {http://eudml.org/doc/273182},

volume = {47},

year = {2013},

}

TY - JOUR

AU - Yaguchi, Takaharu

TI - Lagrangian approach to deriving energy-preserving numerical schemes for the Euler–Lagrange partial differential equations

JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

PY - 2013

PB - EDP-Sciences

VL - 47

IS - 5

SP - 1493

EP - 1513

AB - We propose a Lagrangian approach to deriving energy-preserving finite difference schemes for the Euler–Lagrange partial differential equations. Noether’s theorem states that the symmetry of time translation of Lagrangians yields the energy conservation law. We introduce a unique viewpoint on this theorem: “the symmetry of time translation of Lagrangians derives the Euler–Lagrange equation and the energy conservation law, simultaneously.” The proposed method is a combination of a discrete counter part of this statement and the discrete gradient method. It is also shown that the symmetry of space translation derives momentum-preserving schemes. Finally, we discuss the existence of discrete local conservation laws.

LA - eng

KW - discrete gradient method; energy-preserving integrator; finite difference method; lagrangian mechanics; Lagrangian mechanics; Hamilton-Jacobi equation; conservation law

UR - http://eudml.org/doc/273182

ER -

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