On the solution of Maxwell's equations in polygonal domains
Identifieur interne : 001E30 ( Istex/Corpus ); précédent : 001E29; suivant : 001E31On the solution of Maxwell's equations in polygonal domains
Auteurs : Boniface NkemziSource :
- Mathematical Methods in the Applied Sciences [ 0170-4214 ] ; 2006-06.
English descriptors
- Teeft :
- Appl, Asymptotic behaviour, Boundary conditions, Boundary value problem, Boundary value problems, Cients, Circular sector, Convergence, Copyright, Corner point, Corner points, Discrete fourier transformation, Discretization, Domain, Elliptic, Elliptic boundary value problems, Error estimates, Fourier, Galerkin approximation, Inequality, Interior angle, Interpolation, Interpolation error, John wiley sons, Local mesh, Math, Mathematical methods, Maxwell equations, Meth, Nite, Nite element approximation, Nite element discretization, Nite element method, Nite element methods, Nite element solutions, Nite elements, Nkemzi, Nodal, Numerical analysis, Polygonal, Polygonal plane domain, Polygonal plane domains, Polyhedral domains, Regular part, Regular solutions, Regularity, Sesquilinear form, Siam journal, Singular part, Singularity, Singularity function, Singularity functions, Springer, Step size function, Triangulation, Unique numbers, Unique solution, Variational, Variational problem, Weak solution, Wiley.
Abstract
This paper is concerned with the structure of the singular and regular parts of the solution of time‐harmonic Maxwell's equations in polygonal plane domains and their effective numerical treatment. The asymptotic behaviour of the solution near corner points of the domain is studied by means of discrete Fourier transformation and it is proved that the solution of the boundary value problem does not belong locally to H2 when the boundary of the domain has non‐acute angles. A splitting of the solution into a regular part belonging to the space H2, and an explicitly described singular part is presented. For the numerical treatment of the boundary value problem, we propose a finite element discretization which combines local mesh grading and the singular field methods and derive a priori error estimates that show optimal convergence as known for the classical finite element method for problems with regular solutions. Copyright © 2006 John Wiley & Sons, Ltd.
Url:
DOI: 10.1002/mma.717
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ISTEX:82B450821AECDFD885D7944AE5B6C3C6C1EBA1C8Le document en format XML
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The asymptotic behaviour of the solution near corner points of the domain is studied by means of discrete Fourier transformation and it is proved that the solution of the boundary value problem does not belong locally to <hi rend="italic">H</hi><hi rend="superscript">2</hi> when the boundary of the domain has non‐acute angles. A splitting of the solution into a regular part belonging to the space <hi rend="italic">H</hi><hi rend="superscript">2</hi>, and an explicitly described singular part is presented. For the numerical treatment of the boundary value problem, we propose a finite element discretization which combines local mesh grading and the singular field methods and derive <hi rend="italic">a priori</hi> error estimates that show optimal convergence as known for the classical finite element method for problems with regular solutions. 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The asymptotic behaviour of the solution near corner points of the domain is studied by means of discrete Fourier transformation and it is proved that the solution of the boundary value problem does not belong locally to <i>H</i><sup>2</sup> when the boundary of the domain has non‐acute angles. A splitting of the solution into a regular part belonging to the space <i>H</i><sup>2</sup>, and an explicitly described singular part is presented. For the numerical treatment of the boundary value problem, we propose a finite element discretization which combines local mesh grading and the singular field methods and derive <i>a priori</i> error estimates that show optimal convergence as known for the classical finite element method for problems with regular solutions. 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The asymptotic behaviour of the solution near corner points of the domain is studied by means of discrete Fourier transformation and it is proved that the solution of the boundary value problem does not belong locally to H2 when the boundary of the domain has non‐acute angles. A splitting of the solution into a regular part belonging to the space H2, and an explicitly described singular part is presented. For the numerical treatment of the boundary value problem, we propose a finite element discretization which combines local mesh grading and the singular field methods and derive a priori error estimates that show optimal convergence as known for the classical finite element method for problems with regular solutions. Copyright © 2006 John Wiley & Sons, Ltd.</abstract><note type="funding">INRIA</note><note type="funding">Ministry of Higher Education (MINESUP)</note><subject lang="en"><genre>keywords</genre><topic>Maxwell's equations</topic><topic>corner singularities</topic><topic>finite element method</topic><topic>singular field method</topic><topic>graded mesh refinement</topic><topic>error estimates</topic></subject><relatedItem type="host"><titleInfo><title>Mathematical Methods in the Applied Sciences</title></titleInfo><titleInfo type="abbreviated"><title>Math. Meth. Appl. Sci.</title></titleInfo><genre type="journal" authority="ISTEX" authorityURI="https://publication-type.data.istex.fr" valueURI="https://publication-type.data.istex.fr/ark:/67375/JMC-0GLKJH51-B">journal</genre><subject><genre>article-category</genre><topic>Research Article</topic></subject><identifier type="ISSN">0170-4214</identifier><identifier type="eISSN">1099-1476</identifier><identifier type="DOI">10.1002/(ISSN)1099-1476</identifier><identifier type="PublisherID">MMA</identifier><part><date>2006</date><detail type="volume"><caption>vol.</caption><number>29</number></detail><detail type="issue"><caption>no.</caption><number>9</number></detail><extent unit="pages"><start>1053</start><end>1080</end><total>28</total></extent></part></relatedItem><identifier type="istex">82B450821AECDFD885D7944AE5B6C3C6C1EBA1C8</identifier><identifier type="ark">ark:/67375/WNG-9NRSGS9Z-5</identifier><identifier type="DOI">10.1002/mma.717</identifier><identifier type="ArticleID">MMA717</identifier><accessCondition type="use and reproduction" contentType="copyright">Copyright © 2006 John Wiley & Sons, Ltd.</accessCondition><recordInfo><recordContentSource authority="ISTEX" authorityURI="https://loaded-corpus.data.istex.fr" valueURI="https://loaded-corpus.data.istex.fr/ark:/67375/XBH-L0C46X92-X">wiley</recordContentSource><recordOrigin>John Wiley & Sons, Ltd.</recordOrigin></recordInfo></mods><json:item><extension>json</extension><original>false</original><mimetype>application/json</mimetype><uri>https://api.istex.fr/ark:/67375/WNG-9NRSGS9Z-5/record.json</uri></json:item></metadata><serie></serie></istex></record>Pour manipuler ce document sous Unix (Dilib)
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