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.
Conservación de invariantes de la ecuación de Schrödinger no lineal por el método LDG
Sergio Gomez
2018-01-01
Abstract
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.File in questo prodotto:
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