Optimal convergence recovery for the Fourier-finite-element approximation of Maxwell's equations in nonsmooth axisymmetric domains
type: Item
instance of: scholarly article
title: Optimal convergence recovery for the Fourier-finite-element approximation of Maxwell's equations in nonsmooth axisymmetric domains
zbMATH Open document ID: 1125.65096
author: Boniface Nkemzi
published in: Applied Numerical Mathematics
publication date: 2007-07-23T00:00:00Z
review text: The paper is concerned with the numerical approximation of the time harmonic Maxwell's equations in the case of an axisymmetric domain with edges and conical points on the boundary. The method used is the Fourier-finite-element method: the solution is expanded as a Fourier series with respect to the rotational angle using trigonometric polynomials and then the Fourier coefficients on the plain meridian domain are approximated by means of the finite element method. Error estimates in the \(H^1\)-norm are given when using piecewise linear polynomial shape functions. For domains with reentrant edges and conical points, it is shown that a combination of the singular function method with the finite element method on locally graded meshes for the approximation of the two-dimensional solutions would yield an optimal convergence rate.
reviewed by: Ana M. Alonso Rodriguez
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 35Q60
Mathematics Subject Classification ID: 78A25
Mathematics Subject Classification ID: 78M10
zbMATH DE Number: 5173636
zbMATH Keywords: Maxwell's equations
zbMATH Keywords: finite element method
zbMATH Keywords: Fourier analysis
zbMATH Keywords: singularities of the solution
zbMATH Keywords: error estimates
zbMATH Keywords: convergence
MaRDI profile type: Publication
full work available at URL: j.apnum.2006.09.006
OpenAlex ID: W2069895161
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DOI: 10.1016/J.APNUM.2006.09.006
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description: scientific article; zbMATH DE number 5173636