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

Georgios E. Zouraris

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2001)

  • Volume: 35, Issue: 3, page 389-405
  • ISSN: 0764-583X

Abstract

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We discretize the nonlinear Schrödinger equation, with Dirichlet boundary conditions, by a linearly implicit 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.

How to cite

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Zouraris, Georgios E.. "On the convergence of a linear two-step finite element method for the nonlinear Schrödinger equation." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 35.3 (2001): 389-405. <http://eudml.org/doc/194055>.

@article{Zouraris2001,
abstract = {We discretize the nonlinear Schrödinger equation, with Dirichlet boundary conditions, by a linearly implicit 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.},
author = {Zouraris, Georgios E.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {nonlinear Schrödinger equation; two-step time discretization; linearly implicit method; finite element method; $L^2$ and $H^1$ error estimates; optimal order of convergence; convergence; error bounds},
language = {eng},
number = {3},
pages = {389-405},
publisher = {EDP-Sciences},
title = {On the convergence of a linear two-step finite element method for the nonlinear Schrödinger equation},
url = {http://eudml.org/doc/194055},
volume = {35},
year = {2001},
}

TY - JOUR
AU - Zouraris, Georgios E.
TI - On the convergence of a linear two-step finite element method for the nonlinear Schrödinger equation
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2001
PB - EDP-Sciences
VL - 35
IS - 3
SP - 389
EP - 405
AB - We discretize the nonlinear Schrödinger equation, with Dirichlet boundary conditions, by a linearly implicit 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.
LA - eng
KW - nonlinear Schrödinger equation; two-step time discretization; linearly implicit method; finite element method; $L^2$ and $H^1$ error estimates; optimal order of convergence; convergence; error bounds
UR - http://eudml.org/doc/194055
ER -

References

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