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

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

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

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topZouraris, 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 -

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