Solving a Maxwell interface problem by a local L2projected C0finite element method

Huoyuan Duan; Ping Lin; Roger C E Tan

doi:10.1007/978-3-319-10705-9_79

Solving a Maxwell interface problem by a local L²projected C⁰finite element method

Huoyuan Duan, Ping Lin (Lead / Corresponding author), Roger C E Tan

University of Dundee

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Abstract

In general, the solution of a Maxwell interface problem would not belong to H¹space and the standard C⁰finite element method fails. With the help of local L²projections applied to both the curl and div operators, we propose a new C⁰finite element method which can correctly converge to the non H¹space solution. Stability and error estimates are given.

Original language	English
Title of host publication	Numerical Mathematics and Advanced Applications ENUMATH 2013
Subtitle of host publication	Proceedings of the ENUMATH 2013, the 10th European Conference on Numerical Mathematics and Advanced Applications, Lausanne, August 2013
Editors	Assyr Abdulle, Simone Deparis, Daniel Kressner, Fabio Nobile, Marco Picasso
Place of Publication	Switzerland
Publisher	Springer International Publishing
Pages	795-802
Number of pages	8
ISBN (Electronic)	978319107059
ISBN (Print)	9783319107042
DOIs	https://doi.org/10.1007/978-3-319-10705-9_79
Publication status	Published - 2015

Publication series

Name	Lecture Notes in Computational Science and Engineering
Publisher	Springer
Volume	103
ISSN (Print)	1439-7358

ASJC Scopus subject areas

General Engineering
Computational Mathematics
Modelling and Simulation
Control and Optimization
Discrete Mathematics and Combinatorics

Access to Document

10.1007/978-3-319-10705-9_79

Cite this

Duan, H., Lin, P., & Tan, R. C. E. (2015). Solving a Maxwell interface problem by a local L²projected C⁰finite element method. In A. Abdulle, S. Deparis, D. Kressner, F. Nobile, & M. Picasso (Eds.), Numerical Mathematics and Advanced Applications ENUMATH 2013: Proceedings of the ENUMATH 2013, the 10th European Conference on Numerical Mathematics and Advanced Applications, Lausanne, August 2013 (pp. 795-802). (Lecture Notes in Computational Science and Engineering; Vol. 103). Springer International Publishing. https://doi.org/10.1007/978-3-319-10705-9_79

Duan, Huoyuan ; Lin, Ping ; Tan, Roger C E. / Solving a Maxwell interface problem by a local L²projected C⁰finite element method. Numerical Mathematics and Advanced Applications ENUMATH 2013: Proceedings of the ENUMATH 2013, the 10th European Conference on Numerical Mathematics and Advanced Applications, Lausanne, August 2013. editor / Assyr Abdulle ; Simone Deparis ; Daniel Kressner ; Fabio Nobile ; Marco Picasso. Switzerland : Springer International Publishing, 2015. pp. 795-802 (Lecture Notes in Computational Science and Engineering).

@inbook{73ae1fd7d3224d9b8138bbc214397e42,

title = "Solving a Maxwell interface problem by a local L2projected C0finite element method",

abstract = "In general, the solution of a Maxwell interface problem would not belong to H1space and the standard C0finite element method fails. With the help of local L2projections applied to both the curl and div operators, we propose a new C0finite element method which can correctly converge to the non H1space solution. Stability and error estimates are given.",

author = "Huoyuan Duan and Ping Lin and Tan, {Roger C E}",

year = "2015",

doi = "10.1007/978-3-319-10705-9_79",

language = "English",

isbn = "9783319107042",

series = "Lecture Notes in Computational Science and Engineering",

publisher = "Springer International Publishing",

pages = "795--802",

editor = "Assyr Abdulle and Simone Deparis and Daniel Kressner and Fabio Nobile and Marco Picasso",

booktitle = "Numerical Mathematics and Advanced Applications ENUMATH 2013",

address = "Switzerland",

}

Duan, H, Lin, P & Tan, RCE 2015, Solving a Maxwell interface problem by a local L²projected C⁰finite element method. in A Abdulle, S Deparis, D Kressner, F Nobile & M Picasso (eds), Numerical Mathematics and Advanced Applications ENUMATH 2013: Proceedings of the ENUMATH 2013, the 10th European Conference on Numerical Mathematics and Advanced Applications, Lausanne, August 2013. Lecture Notes in Computational Science and Engineering, vol. 103, Springer International Publishing, Switzerland, pp. 795-802. https://doi.org/10.1007/978-3-319-10705-9_79

Solving a Maxwell interface problem by a local L²projected C⁰finite element method. / Duan, Huoyuan; Lin, Ping (Lead / Corresponding author); Tan, Roger C E.
Numerical Mathematics and Advanced Applications ENUMATH 2013: Proceedings of the ENUMATH 2013, the 10th European Conference on Numerical Mathematics and Advanced Applications, Lausanne, August 2013. ed. / Assyr Abdulle; Simone Deparis; Daniel Kressner; Fabio Nobile; Marco Picasso. Switzerland: Springer International Publishing, 2015. p. 795-802 (Lecture Notes in Computational Science and Engineering; Vol. 103).

Research output: Chapter in Book/Report/Conference proceeding › Chapter

TY - CHAP

T1 - Solving a Maxwell interface problem by a local L2projected C0finite element method

AU - Duan, Huoyuan

AU - Lin, Ping

AU - Tan, Roger C E

PY - 2015

Y1 - 2015

N2 - In general, the solution of a Maxwell interface problem would not belong to H1space and the standard C0finite element method fails. With the help of local L2projections applied to both the curl and div operators, we propose a new C0finite element method which can correctly converge to the non H1space solution. Stability and error estimates are given.

AB - In general, the solution of a Maxwell interface problem would not belong to H1space and the standard C0finite element method fails. With the help of local L2projections applied to both the curl and div operators, we propose a new C0finite element method which can correctly converge to the non H1space solution. Stability and error estimates are given.

UR - http://www.scopus.com/inward/record.url?scp=84919819750&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-10705-9_79

DO - 10.1007/978-3-319-10705-9_79

M3 - Chapter

AN - SCOPUS:84919819750

SN - 9783319107042

T3 - Lecture Notes in Computational Science and Engineering

SP - 795

EP - 802

BT - Numerical Mathematics and Advanced Applications ENUMATH 2013

A2 - Abdulle, Assyr

A2 - Deparis, Simone

A2 - Kressner, Daniel

A2 - Nobile, Fabio

A2 - Picasso, Marco

PB - Springer International Publishing

CY - Switzerland

ER -

Duan H, Lin P, Tan RCE. Solving a Maxwell interface problem by a local L²projected C⁰finite element method. In Abdulle A, Deparis S, Kressner D, Nobile F, Picasso M, editors, Numerical Mathematics and Advanced Applications ENUMATH 2013: Proceedings of the ENUMATH 2013, the 10th European Conference on Numerical Mathematics and Advanced Applications, Lausanne, August 2013. Switzerland: Springer International Publishing. 2015. p. 795-802. (Lecture Notes in Computational Science and Engineering). doi: 10.1007/978-3-319-10705-9_79