Resumo

CASTILLO, P.E.  e  GOMEZ, S.A.. Conservación de invariantes de la ecuación de Schrödinger no lineal por el método LDG. Rev. mex. fís. E [online]. 2018, vol.64, n.1, pp.52-60. ISSN 1870-3542.

Conservation of the energy and the Hamiltonian of a general non linear Schrödinger equation is analyzed for the finite element method “Local Discontinuous Galerkin” spatial discretization. Conservation of the discrete analogue of these quantities is also proved for the fully discrete problem using the modified Crank-Nicolson method as time marching scheme. The theoretical results are validated on a series of problems for different nonlinear potentials.

Palavras-chave : Nonlinear Schrödinger equation; Local Discontinuous Galerkin method; energy and Hamiltonian conservation; modified Crank-Nicolson.

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