On the solution of Maxwell's equations in polygonal domains
Identifieur interne : 005421 ( Main/Exploration ); précédent : 005420; suivant : 005422On the solution of Maxwell's equations in polygonal domains
Auteurs : Boniface Nkemzi [Cameroun]Source :
- 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
Affiliations:
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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. 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