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

5 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

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10.1093/imanum/drx060

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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

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DO - 10.1093/imanum/drx060

M3 - Journal article

AN - SCOPUS:85057274209

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JF - IMA Journal of Numerical Analysis

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

Abstract

Keywords

ASJC Scopus subject areas

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