Error estimates of Crank-Nicolson Galerkin method for the time-dependent Maxwell-Schrödinger equations under the Lorentz gauge

Chupeng Ma; Liqun Cao; Yanping Lin

doi:10.1093/imanum/drx060

Error estimates of Crank-Nicolson Galerkin method for the time-dependent Maxwell-Schrödinger equations under the Lorentz gauge

Chupeng Ma
, Liqun Cao
, Yanping Lin

Research output: Journal article publication › Journal article › Academic research › peer-review

6 Citations (Scopus)

Abstract

In this article, we study a numerical method and its convergence for solving the time-dependent Maxwell-Schrödinger equations under the Lorentz gauge. An alternating Crank-Nicolson finite-element method for solving the problem is presented and an optimal error estimate for the numerical algorithm is obtained by a mathematical inductive method. Numerical experiments are then carried out to confirm the theoretical results.

Original language	English
Pages (from-to)	2074-2104
Number of pages	31
Journal	IMA Journal of Numerical Analysis
Volume	38
Issue number	4
DOIs	https://doi.org/10.1093/imanum/drx060
Publication status	Published - 16 Oct 2018

Keywords

Crank-Nicolson
error estimates
Galerkin method
Maxwell-Schrödinger

ASJC Scopus subject areas

General Mathematics
Computational Mathematics
Applied Mathematics

More information

10.1093/imanum/drx060

Cite this

@article{60d0840b6723459eb62cba5b6c2075fb,

title = "Error estimates of Crank-Nicolson Galerkin method for the time-dependent Maxwell-Schr{\"o}dinger equations under the Lorentz gauge",

abstract = "In this article, we study a numerical method and its convergence for solving the time-dependent Maxwell-Schr{\"o}dinger equations under the Lorentz gauge. An alternating Crank-Nicolson finite-element method for solving the problem is presented and an optimal error estimate for the numerical algorithm is obtained by a mathematical inductive method. Numerical experiments are then carried out to confirm the theoretical results.",

keywords = "Crank-Nicolson, error estimates, Galerkin method, Maxwell-Schr{\"o}dinger",

author = "Chupeng Ma and Liqun Cao and Yanping Lin",

year = "2018",

month = oct,

day = "16",

doi = "10.1093/imanum/drx060",

language = "English",

volume = "38",

pages = "2074--2104",

journal = "IMA Journal of Numerical Analysis",

issn = "0272-4979",

publisher = "Oxford University Press",

number = "4",

}

TY - JOUR

T1 - Error estimates of Crank-Nicolson Galerkin method for the time-dependent Maxwell-Schrödinger equations under the Lorentz gauge

AU - Ma, Chupeng

AU - Cao, Liqun

AU - Lin, Yanping

PY - 2018/10/16

Y1 - 2018/10/16

N2 - In this article, we study a numerical method and its convergence for solving the time-dependent Maxwell-Schrödinger equations under the Lorentz gauge. An alternating Crank-Nicolson finite-element method for solving the problem is presented and an optimal error estimate for the numerical algorithm is obtained by a mathematical inductive method. Numerical experiments are then carried out to confirm the theoretical results.

AB - In this article, we study a numerical method and its convergence for solving the time-dependent Maxwell-Schrödinger equations under the Lorentz gauge. An alternating Crank-Nicolson finite-element method for solving the problem is presented and an optimal error estimate for the numerical algorithm is obtained by a mathematical inductive method. Numerical experiments are then carried out to confirm the theoretical results.

KW - Crank-Nicolson

KW - error estimates

KW - Galerkin method

KW - Maxwell-Schrödinger

UR - https://www.scopus.com/pages/publications/85057274209

U2 - 10.1093/imanum/drx060

DO - 10.1093/imanum/drx060

M3 - Journal article

AN - SCOPUS:85057274209

SN - 0272-4979

VL - 38

SP - 2074

EP - 2104

JO - IMA Journal of Numerical Analysis

JF - IMA Journal of Numerical Analysis

IS - 4

ER -

Error estimates of Crank-Nicolson Galerkin method for the time-dependent Maxwell-Schrödinger equations under the Lorentz gauge

Abstract

Keywords

ASJC Scopus subject areas

More information

Other files and links

Fingerprint

Cite this