Edge finite elements for the approximation of Maxwell resolvent operator

Daniele Boffi; Lucia Gastaldi

Displaying similar documents to “Edge finite elements for the approximation of Maxwell resolvent operator”

Spurious-free approximations of electromagnetic eigenproblems by means of Nedelec-type elements

Salvatore Caorsi, Paolo Fernandes, Mirco Raffetto (2001)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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By using an inductive procedure we prove that the Galerkin finite element approximations of electromagnetic eigenproblems modelling cavity resonators by elements of any fixed order of either Nedelec’s edge element family on tetrahedral meshes are convergent and free of spurious solutions. This result is not new but is proved under weaker hypotheses, which are fulfilled in most of engineering applications. The method of the proof is new, instead, and shows how families of spurious-free...

Finite element approximation for a div-rot system with mixed boundary conditions in non-smooth plane domains

Michal Křížek, Pekka Neittaanmäki (1984)

Aplikace matematiky

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The authors examine a finite element method for the numerical approximation of the solution to a div-rot system with mixed boundary conditions in bounded plane domains with piecewise smooth boundary. The solvability of the system both in an infinite and finite dimensional formulation is proved. Piecewise linear element fields with pointwise boundary conditions are used and their approximation properties are studied. Numerical examples indicating the accuracy of the method are given. ...

On time-harmonic Maxwell equations with nonhomogeneous conductivities: Solvability and FE-approximation

Michal Křížek, Pekka Neittaanmäki (1989)

Aplikace matematiky

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The solvability of time-harmonic Maxwell equations in the 3D-case with nonhomogeneous conductivities is considered by adapting Sobolev space technique and variational formulation of the problem in question. Moreover, a finite element approximation is presented in the 3D-case together with an error estimate in the energy norm. Some remarks are given to the 2D-problem arising from geophysics.

Mixed methods for the approximation of liquid crystal flows

Chun Liu, Noel J. Walkington (2002)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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The numerical solution of the flow of a liquid crystal governed by a particular instance of the Ericksen–Leslie equations is considered. Convergence results for this system rely crucially upon energy estimates which involve $H^{2} (Ω)$ norms of the director field. We show how a mixed method may be used to eliminate the need for Hermite finite elements and establish convergence of the method.

Mixed finite element approximation of an MHD problem involving conducting and insulating regions : the 2D case

Jean Luc Guermond, Peter D. Minev (2002)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We show that the Maxwell equations in the low frequency limit, in a domain composed of insulating and conducting regions, has a saddle point structure, where the electric field in the insulating region is the Lagrange multiplier that enforces the curl-free constraint on the magnetic field. We propose a mixed finite element technique for solving this problem, and we show that, under mild regularity assumption on the data, Lagrange finite elements can be used as an alternative to edge...