Optimal convergence recovery for the Fourier-finite-element approximation of Maxwell's equations in nonsmooth axisymmetric domains

DOI10.1016/j.apnum.2006.09.006zbMath1125.65096OpenAlexW2069895161MaRDI QIDQ997215

Boniface Nkemzi

Publication date: 23 July 2007

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2006.09.006

zbMATH Keywords

convergenceerror estimatesfinite element methodFourier analysisMaxwell's equationssingularities of the solution

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory (78M10) Electromagnetic theory (general) (78A25)

Related Items (5)

Multigrid in \(\boldsymbol H(\text{div})\) on axisymmetric domains ⋮ A NUMERICAL METHOD FOR 3D TIME-DEPENDENT MAXWELL’S EQUATIONS IN AXISYMMETRIC SINGULAR DOMAINS WITH ARBITRARY DATA ⋮ Numerical solution to the 3D static Maxwell equations in axisymmetric singular domains with arbitrary data ⋮ On the coefficients of the singularities of the solution of Maxwell's equations near polyhedral edges ⋮ The Fourier-finite element method for the Poisson problem on a non-convex polyhedral cylinder

Cites Work

• The Fourier singular complement method for the Poisson problem. II: Axisymmetric domains
• Mixed finite elements in \(\mathbb{R}^3\)
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• Singularities of electromagnetic fields in polyhedral domains
• Résolution d’un problème aux limites dans un ouvert axisymétrique par éléments finis en $r, z$ et séries de Fourier en $\theta $
• A Singular Field Method for the Solution of Maxwell's Equations in Polyhedral Domains
• Partial Fourier approximation of the Lamé equations in axisymmetric domains
• Resolution of the Maxwell equations in a domain with reentrant corners
• On solution of Lamé equations in axisymmetric domains with conical points
• The Fourier-Finite-Element Method for Poisson’s Equation in Axisymmetric Domains with Edges
• A Singular Field Method for Maxwell's Equations: Numerical Aspects for 2D Magnetostatics
• On the solution of Maxwell's equations in axisymmetric domains with edges
• On the solution of Maxwell's equations in polygonal domains
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