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 (2010)

  • 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 L2 norm. We prove optimal order a priori error estimates in the L2 and H1 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 35.3 (2010): 389-405. <http://eudml.org/doc/197599>.

@article{Zouraris2010,
abstract = { We discretize the nonlinear Schrödinger equation, with Dirichlet boundary conditions, by a linearly implicit two-step finite element method which conserves the L2 norm. We prove optimal order a priori error estimates in the L2 and H1 norms, under mild mesh conditions for two and three space dimensions. },
author = {Zouraris, Georgios E.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Nonlinear Schrödinger equation; two-step time discretization; linearly implicit method; finite element method; L2 and H1 error estimates; optimal order of convergence.; nonlinear Schrödinger equation; convergence; error bounds},
language = {eng},
month = {3},
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/197599},
volume = {35},
year = {2010},
}

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
DA - 2010/3//
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 L2 norm. We prove optimal order a priori error estimates in the L2 and H1 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; L2 and H1 error estimates; optimal order of convergence.; nonlinear Schrödinger equation; convergence; error bounds
UR - http://eudml.org/doc/197599
ER -

References

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