Approximation of the eigenvalue problem for the time harmonic Maxwell system by continuous Lagrange finite elements

DOI10.1090/S0025-5718-2011-02464-6zbMath1227.78020OpenAlexW2090343972MaRDI QIDQ3094275

Andrea Bonito, Jean-Luc Guermond

Publication date: 24 October 2011

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-2011-02464-6

zbMATH Keywords

eigenvaluefinite elementsMaxwell equationsspectral approximation

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory (78M10) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25) Maxwell equations (35Q61)

Related Items (26)

Finite Element Methods for Maxwell's Equations ⋮ Two Variants of Stabilized Nodal-Based FEM for the Magnetic Induction Problem ⋮ Nodal finite element de Rham complexes ⋮ Stabilized nodal-based finite element methods for the magnetic induction problem ⋮ Analysis of an unconditionally convergent stabilized finite element formulation for incompressible magnetohydrodynamics ⋮ Computation of Maxwell singular solution by nodal-continuous elements ⋮ Mixed finite elements for electromagnetic analysis ⋮ Nodal-based finite element methods with local projection stabilization for linearized incompressible magnetohydrodynamics ⋮ Two-level coupled and decoupled parallel correction methods for stationary incompressible magnetohydrodynamics ⋮ A Unified Error Analysis of Hybridizable Discontinuous Galerkin Methods for the Static Maxwell Equations ⋮ Analysis of a continuous finite element method for \(H(\mathrm{curl},\mathrm{div})\)-elliptic interface problem ⋮ Variational methods for solving numerically magnetostatic systems ⋮ A Mixed $H^1$-Conforming Finite Element Method for Solving Maxwell's Equations with Non-$H^1$ Solution ⋮ A combined nodal continuous-discontinuous finite element formulation for the Maxwell problem ⋮ New Mixed Elements for Maxwell Equations ⋮ A mixed finite element method with exactly divergence-free velocities for incompressible magnetohydrodynamics ⋮ Local two-sided bounds for eigenvalues of self-adjoint operators ⋮ Mixed Finite Element Method with Gauss's Law Enforced for the Maxwell Eigenproblem ⋮ Regularity of the Maxwell equations in heterogeneous media and Lipschitz domains ⋮ Decoupled schemes for unsteady MHD equations. II: Finite element spatial discretization and numerical implementation ⋮ Effects of discontinuous magnetic permeability on magnetodynamic problems ⋮ Numerical simulation of the von Kármán sodium dynamo experiment ⋮ Approximation of PDE eigenvalue problems involving parameter dependent matrices ⋮ A Finite Element Method for a Curlcurl-Graddiv Eigenvalue Interface Problem ⋮ A mixed method for Maxwell eigenproblem ⋮ An Interior Penalty Method with C⁰Finite Elements for the Approximation of the Maxwell Equations in Heterogeneous Media: Convergence Analysis with Minimal Regularity

Uses Software

• ARPACK

Cites Work

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