Interpolation estimates for edge finite elements and application to band gap computation

DOI10.1016/j.apnum.2006.03.014zbMath1100.65088OpenAlexW2123309335MaRDI QIDQ2507721

Daniele Boffi, Lucia Gastaldi

Publication date: 5 October 2006

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

Full work available at URL: https://doi.org/10.1016/j.apnum.2006.03.014

zbMATH Keywords

numerical exampleserror boundsMaxwell's equationsinterpolation estimatesphotonic crystalsedge finite elements

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) Error bounds for boundary value problems involving PDEs (65N15) 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 (4)

Local decay rates of best-approximation errors using vector-valued finite elements for fields with low regularity and integrable curl or divergence ⋮ Analysis of the edge finite element approximation of the Maxwell equations with low regularity solutions ⋮ A mixed finite element formulation for compressible finite hyperelasticity with two fibre family reinforcement ⋮ Determination of electromagnetic Bloch variety in a medium with frequency-dependent coefficients

Cites Work

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• Modified edge finite elements for photonic crystals
• Mixed finite elements in \(\mathbb{R}^3\)
• A finite element method for approximating the time-harmonic Maxwell equations
• Fortin operator and discrete compactness for edge elements
• Finite elements in computational electromagnetism
• Singularities of Maxwell interface problems
• Polynomial Approximation of Functions in Sobolev Spaces
• Vector potentials in three-dimensional non-smooth domains
• An optimal domain decomposition preconditioner for low-frequency time-harmonic Maxwell equations
• Finite Element Methods for Maxwell's Equations
• QuadrilateralH(div) Finite Elements

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