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

被引：4

作者：

Ma, Chupeng ^{[1
,2
]}

Cao, Liqun ^{[1
,2
]}

Lin, Yanping ^{[3
]}

机构：

[1] Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, LSEC, Beijing 100190, Peoples R China

[2] Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China

[3] Hong Kong Polytech Univ, Dept Appl Math, Kowloon, Hong Kong, Peoples R China

来源：

IMA JOURNAL OF NUMERICAL ANALYSIS | 2018年 / 38卷 / 04期

关键词：

error estimates; Crank-Nicolson; Galerkin method; Maxwell-Schrodinger; GINZBURG-LANDAU EQUATIONS; MODIFIED WAVE-OPERATORS; GLOBAL EXISTENCE; COUPLED MAXWELL; SIMULATION; EFFICIENT; INTENSE; MODEL;

D O I：

10.1093/imanum/drx060

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we study a numerical method and its convergence for solving the time-dependent Maxwell-Schrodinger 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.

引用

页码：2074 / 2104

页数：31

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