A third order linearized BDF scheme for Maxwell’s equations with nonlinear conductivity using finite element method

Changhui Yao; Yanping Lin; Cheng Wang; Yanli Kou

A third order linearized BDF scheme for Maxwell’s equations with nonlinear conductivity using finite element method

Changhui Yao, Yanping Lin, Cheng Wang, Yanli Kou

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

Abstract

In this paper, we study a third order accurate linearized backward differential formula (BDF) type scheme for the nonlinear Maxwell’s equations, using the Nédelec finite element approximation in space. A purely explicit treatment of the nonlinear term greatly simplifies the computational effort, since we only need to solve a constant-coefficient linear system at each time step. An optimal L2error estimate is presented, via a linearized stability analysis for the numerical error function, under a condition for the time step, τ ≤ C0∗h2for a fixed constant C0∗. Numerical results are provided to confirm our theoretical analysis and demonstrate the high order accuracy and stability (convergence) of the linearized BDF finite element method.

Original language	English
Pages (from-to)	511-531
Number of pages	21
Journal	International Journal of Numerical Analysis and Modeling
Volume	14
Issue number	4-5
Publication status	Published - 1 Jan 2017

Keywords

Convergence analysis and optimal error estimate
Linearized stability analysis
Maxwell’s equations with nonlinear conductivity
The third order BDF scheme

ASJC Scopus subject areas

Numerical Analysis

Cite this

@article{0dc9a7a05b09473b8ba85ffe5082a6e5,

title = "A third order linearized BDF scheme for Maxwell{\textquoteright}s equations with nonlinear conductivity using finite element method",

abstract = "In this paper, we study a third order accurate linearized backward differential formula (BDF) type scheme for the nonlinear Maxwell{\textquoteright}s equations, using the N{\'e}delec finite element approximation in space. A purely explicit treatment of the nonlinear term greatly simplifies the computational effort, since we only need to solve a constant-coefficient linear system at each time step. An optimal L2error estimate is presented, via a linearized stability analysis for the numerical error function, under a condition for the time step, τ ≤ C0∗h2for a fixed constant C0∗. Numerical results are provided to confirm our theoretical analysis and demonstrate the high order accuracy and stability (convergence) of the linearized BDF finite element method.",

keywords = "Convergence analysis and optimal error estimate, Linearized stability analysis, Maxwell{\textquoteright}s equations with nonlinear conductivity, The third order BDF scheme",

author = "Changhui Yao and Yanping Lin and Cheng Wang and Yanli Kou",

year = "2017",

month = jan,

day = "1",

language = "English",

volume = "14",

pages = "511--531",

journal = "International Journal of Numerical Analysis and Modeling",

issn = "1705-5105",

publisher = "University of Alberta",

number = "4-5",

}

A third order linearized BDF scheme for Maxwell’s equations with nonlinear conductivity using finite element method. / Yao, Changhui; Lin, Yanping; Wang, Cheng et al.
In: International Journal of Numerical Analysis and Modeling, Vol. 14, No. 4-5, 01.01.2017, p. 511-531.

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

TY - JOUR

T1 - A third order linearized BDF scheme for Maxwell’s equations with nonlinear conductivity using finite element method

AU - Yao, Changhui

AU - Lin, Yanping

AU - Wang, Cheng

AU - Kou, Yanli

PY - 2017/1/1

Y1 - 2017/1/1

N2 - In this paper, we study a third order accurate linearized backward differential formula (BDF) type scheme for the nonlinear Maxwell’s equations, using the Nédelec finite element approximation in space. A purely explicit treatment of the nonlinear term greatly simplifies the computational effort, since we only need to solve a constant-coefficient linear system at each time step. An optimal L2error estimate is presented, via a linearized stability analysis for the numerical error function, under a condition for the time step, τ ≤ C0∗h2for a fixed constant C0∗. Numerical results are provided to confirm our theoretical analysis and demonstrate the high order accuracy and stability (convergence) of the linearized BDF finite element method.

AB - In this paper, we study a third order accurate linearized backward differential formula (BDF) type scheme for the nonlinear Maxwell’s equations, using the Nédelec finite element approximation in space. A purely explicit treatment of the nonlinear term greatly simplifies the computational effort, since we only need to solve a constant-coefficient linear system at each time step. An optimal L2error estimate is presented, via a linearized stability analysis for the numerical error function, under a condition for the time step, τ ≤ C0∗h2for a fixed constant C0∗. Numerical results are provided to confirm our theoretical analysis and demonstrate the high order accuracy and stability (convergence) of the linearized BDF finite element method.

KW - Convergence analysis and optimal error estimate

KW - Linearized stability analysis

KW - Maxwell’s equations with nonlinear conductivity

KW - The third order BDF scheme

UR - http://www.scopus.com/inward/record.url?scp=85025069672&partnerID=8YFLogxK

M3 - Journal article

SN - 1705-5105

VL - 14

SP - 511

EP - 531

JO - International Journal of Numerical Analysis and Modeling

JF - International Journal of Numerical Analysis and Modeling

IS - 4-5

ER -

A third order linearized BDF scheme for Maxwell’s equations with nonlinear conductivity using finite element method

Abstract

Keywords

ASJC Scopus subject areas

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