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On the convergence of a linear two-step finite element methodfor the nonlinear Schrödinger equation

Published online by Cambridge University Press:  15 April 2002

Georgios E. Zouraris
Georgios E. Zouraris*
Affiliation:
Department of Numerical Analysis and Computing Science (NADA), Royal Institute of Technology (KTH), 10044 Stockholm, Sweden. : Centre de Recherche en Mathématiques de la Décision (CEREMADE), UMR CNRS 7534, Université de Paris IX-Dauphine, Place du Maréchal de Lattre-de-Tassigny, 75775 Paris Cedex 16, France.
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Abstract

We discretize the nonlinear Schrödinger equation,with Dirichlet boundary conditions, by a linearlyimplicit two-step finite element method which conserves the L 2 norm. We prove optimal order a priori error estimates in the L 2 and H 1 norms, under mild mesh conditions for two and three space dimensions.

Keywords

Nonlinear Schrödinger equationtwo-step time discretizationlinearly implicit methodfinite element methodL 2 and H 1 error estimatesoptimal order of convergence.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 35 , Issue 3 , May 2001 , pp. 389 - 405
Copyright
© EDP Sciences, SMAI, 2001

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