Error estimates for a Galerkin method for a coupled nonlinear Schrodinger equations
Bull. Korean Math. Soc.
Published online August 2, 2019
Khaled Omrani and Mohamed Rahmeni
University of Sousse
Abstract : In this paper, we approximate the solution of the coupled nonlinear Schrodinger equations by using a fully discrete finite element scheme based on the standard Galerkin method in space and implicit midpoint discretization in time. The proposed scheme guarantees the conservation of the total mass and the energy. First, a priori error estimates for the fully discrete Galerkin method is derived. Second, the existence of the approximated solution is proved by virtue of the Brouwer fixed point theorem. Moreover, the uniqueness of the solution is shown. Finally, convergence orders of the fully discrete Crank-Nicolson scheme are discussed. The end of the paper is devoted to some numerical experiments.
Keywords : Coupled Schrodinger equations, Galerkin finite element scheme, conservation laws, unique solvability, convergence.
MSC numbers : 65M06, 65M12, 65M15
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