An Interior Penalty Method with C0Finite Elements for the Approximation of the Maxwell Equations in Heterogeneous Media: Convergence Analysis with Minimal Regularity

DOI10.1051/m2an/2015086zbMath1352.78014OpenAlexW2224192171MaRDI QIDQ2830705

Andrea Bonito, Francky Luddens, Jean-Luc Guermond

Publication date: 28 October 2016

Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1051/m2an/2015086

zbMATH Keywords

eigenvaluefinite elementsdiscontinuous coefficientsMaxwell equationsspectral approximation

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) PDEs in connection with optics and electromagnetic theory (35Q60) 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) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25)

Related Items (13)

Small collaboration: Numerical analysis of electromagnetic problems. Abstracts from the mini-workshop held March 21--27, 2021 (hybrid meeting) ⋮ A Bochev‐Dohrmann‐Gunzburger stabilized method for Maxwell eigenproblem ⋮ A stabilized finite element method on nonaffine grids for time-harmonic Maxwell's equations ⋮ A Mixed $H^1$-Conforming Finite Element Method for Solving Maxwell's Equations with Non-$H^1$ Solution ⋮ New Mixed Elements for Maxwell Equations ⋮ Mixed Finite Element Method with Gauss's Law Enforced for the Maxwell Eigenproblem ⋮ Developing and analyzing new unconditionally stable finite element schemes for Maxwell's equations in complex media ⋮ Unnamed Item ⋮ Two new finite element schemes and their analysis for modeling of wave propagation in graphene ⋮ A mixed method for Maxwell eigenproblem ⋮ Virtual Element approximations of the Vector Potential Formulation of Magnetostatic problems ⋮ Quasi-optimal nonconforming approximation of elliptic PDEs with contrasted coefficients and \(H^{1+r}, r>0\), regularity ⋮ A superconvergent HDG method for the Maxwell equations

Uses Software

• ARPACK
• SFEMaNS

Cites Work

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