DISCRETE COMPACTNESS FOR p AND hp 2D EDGE FINITE ELEMENTS

DOI10.1142/S0218202503003070zbMath1056.65108OpenAlexW1966104551MaRDI QIDQ3043598

Martin Costabel, Daniele Boffi, Leszek F. Demkowicz

Publication date: 6 August 2004

Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218202503003070

zbMATH Keywords

stabilityeigenproblemMaxwell's equationsdiscrete compactness\(hp\) finite elements

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) Estimates of eigenvalues in context of PDEs (35P15) 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 (6)

Integration of \(hp\)-adaptivity and a two-grid solver for electromagnetic problems ⋮ EXPONENTIAL CONVERGENCE OF hp-FEM FOR MAXWELL EQUATIONS WITH WEIGHTED REGULARIZATION IN POLYGONAL DOMAINS ⋮ The hp-BEM with quasi-uniform meshes for the electric field integral equation on polyhedral surfaces: A priori error analysis ⋮ The application of the \(hp\)-finite element method to electromagnetic problems ⋮ A viscosity solution method for Shape-From-Shading without image boundary data ⋮ \(hp\)-vector finite element method for eigenmode analysis of waveguides

Uses Software

• Mathematica

Cites Work

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• A new family of mixed finite elements in \({\mathbb{R}}^ 3\)
• Fortin operator and discrete compactness for edge elements
• Singularities of electromagnetic fields in polyhedral domains
• Discrete compactness and the approximation of Maxwell's equations in $\mathbb{R}^3$
• Mixed and Hybrid Finite Element Methods
• Computational Models of Electromagnetic Resonators: Analysis of Edge Element Approximation
• On the Convergence of Galerkin Finite Element Approximations of Electromagnetic Eigenproblems
• A note on the de Rham complex and a discrete compactness property

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