The approximation of the Maxwell eigenvalue problem using a least-squares method

DOI10.1090/S0025-5718-05-01759-XzbMath1078.65100OpenAlexW1970402902MaRDI QIDQ5315408

James H. Bramble, Joseph E. Pasciak, Tzanio V. Kolev

Publication date: 8 September 2005

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

Full work available at URL: https://doi.org/10.1090/s0025-5718-05-01759-x

zbMATH Keywords

convergencenumerical exampleseigenvaluesMaxwell equationdiv-curl systemsfinite-element least-squares method

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) Estimates of eigenvalues in context of PDEs (35P15) 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) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25)

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Convergence analysis of a Galerkin boundary element method for electromagnetic resonance problems, A least-squares approximation method for the time-harmonic Maxwell equations, Analysis of an unconditionally convergent stabilized finite element formulation for incompressible magnetohydrodynamics, Mixed finite elements for electromagnetic analysis, Numerical approximation based on a decoupled dimensionality reduction scheme for Maxwell eigenvalue problem, A Mixed $H^1$-Conforming Finite Element Method for Solving Maxwell's Equations with Non-$H^1$ Solution, A negative-norm least-squares method for time-harmonic Maxwell equations, Local two-sided bounds for eigenvalues of self-adjoint operators, Mixed Finite Element Method with Gauss's Law Enforced for the Maxwell Eigenproblem, A family of optimal Lagrange elements for Maxwell's equations, A reduced basis method for electromagnetic scattering by multiple particles in three dimensions, A Finite Element Method for a Curlcurl-Graddiv Eigenvalue Interface Problem, A mixed method for Maxwell eigenproblem, Computation of the LBB Constant for the Stokes Equation with a Least-Squares Finite Element Method, Nonlinear magnetohydrodynamics in axisymmetric heterogeneous domains using a Fourier/finite element technique and an interior penalty method, Approximation of the eigenvalue problem for the time harmonic Maxwell system by continuous Lagrange finite elements, An Interior Penalty Method with C⁰Finite Elements for the Approximation of the Maxwell Equations in Heterogeneous Media: Convergence Analysis with Minimal Regularity, Some results on electromagnetic transmission eigenvalues

Uses Software

• lobpcg.m

Cites Work

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