Discontinuous Galerkin and multiscale variational schemes for a coupled damped nonlinear system of Schrödinger equations
Artikel i vetenskaplig tidskrift, 2013

In this article, we study a streamline diffusion-based discontinuous Galerkin approximation for the numerical solution of a coupled nonlinear system of Schrödinger equations and extend the resulting method to a multiscale variational scheme. We prove stability estimates and derive optimal convergence rates due to the maximal available regularity of the exact solution. In the weak formulation, to make the underlying bilinear form coercive, it was necessary to supply the equation system with an artificial viscosity term with a small coefficient of order proportional to a power of mesh size. We justify the theory by implementing an example of an application of the time-dependent Schrödinger equation in the coupled ultrafast laser.

coupled nonlinear Schrödinger equations

discontinuous Galerkin method

multiscale variational scheme



streamline diffusion method


Mohammad Asadzadeh

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

D. Rostamy

Imam Khomeini International University

F. Zabihi

Imam Khomeini International University

Numerical Methods for Partial Differential Equations

0749-159X (ISSN)

Vol. 29 1912-1945