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Journal of Scientific Computing

Erschienen in:

01.08.2014

A New Error Analysis of Crank–Nicolson Galerkin FEMs for a Generalized Nonlinear Schrödinger Equation

verfasst von: Jilu Wang

Erschienen in: Journal of Scientific Computing | Ausgabe 2/2014

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Abstract

In this paper, we study linearized Crank–Nicolson Galerkin FEMs for a generalized nonlinear Schrödinger equation. We present the optimal \(L^2\) error estimate without any time-step restrictions, while previous works always require certain conditions on time stepsize. A key to our analysis is an error splitting, in terms of the corresponding time-discrete system, with which the error is split into two parts, the temporal error and the spatial error. Since the spatial error is \(\tau \)-independent, the numerical solution can be bounded in \(L^{\infty }\)-norm by an inverse inequality unconditionally. Then, the optimal \(L^2\) error estimate can be obtained by a routine method. To confirm our theoretical analysis, numerical results in both two and three dimensional spaces are presented.

Vorheriger Artikel A Class of Incomplete Riemann Solvers Based on Uniform Rational Approximations to the Absolute Value Function

Nächster Artikel A Multilayer Method for the Hydrostatic Navier-Stokes Equations: A Particular Weak Solution

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Titel: A New Error Analysis of Crank–Nicolson Galerkin FEMs for a Generalized Nonlinear Schrödinger Equation
verfasst von: Jilu Wang
Publikationsdatum: 01.08.2014
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 2/2014
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-013-9799-4

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