An isomorphic property of two Hilbert spaces appearing in electromagnetism: Analysis by the mixed formulation

DOI10.1007/BF03167091zbMath0613.46040MaRDI QIDQ4720236

Fumio Kikuchi

Publication date: 1986

Published in: Japan Journal of Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

rotationsfinite element methodLagrange multiplier methodmixed formulationimbedding theoremdivergencesconvex domains with sufficiently smooth boundariesdivergences of functions are square summablenumerical analysis of electromagnetic problems

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Spaces of vector- and operator-valued functions (46E40) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Electromagnetic theory (general) (78A25) Hilbert spaces of continuous, differentiable or analytic functions (46E20) Applications to the sciences (65Z05)

Related Items (7)

An analysis of Nédélec's method for the spatial discretization of Maxwell's equations ⋮ Mixed and penalty formulations for finite element analysis of an eigenvalue problem in electromagnetism ⋮ Unnamed Item ⋮ Discrete compactness and the approximation of Maxwell's equations in $\mathbb{R}^3$ ⋮ Unnamed Item ⋮ Mixed formulations for finite element analysis of magnetostatic and electrostatic problems ⋮ On time-harmonic Maxwell equations with nonhomogeneous conductivities: Solvability and FE-approximation

Cites Work

• Mixed and penalty formulations for finite element analysis of an eigenvalue problem in electromagnetism
• Maxwell's boundary value problem on Riemannian manifolds with nonsmooth boundaries
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