Displaying similar documents to “A mixed–FEM and BEM coupling for a three-dimensional eddy current problem”

Edge finite elements for the approximation of Maxwell resolvent operator

Daniele Boffi, Lucia Gastaldi (2002)

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

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In this paper we consider the Maxwell resolvent operator and its finite element approximation. In this framework it is natural the use of the edge element spaces and to impose the divergence constraint in a weak sense with the introduction of a Lagrange multiplier, following an idea by Kikuchi [14]. We shall review some of the known properties for edge element approximations and prove some new result. In particular we shall prove a uniform convergence in the L 2 norm for the sequence of...

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.

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. ...

Internal finite element approximations in the dual variational method for second order elliptic problems with curved boundaries

Ivan Hlaváček, Michal Křížek (1984)

Aplikace matematiky

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Using the stream function, some finite element subspaces of divergence-free vector functions, the normal components of which vanish on a part of the piecewise smooth boundary, are constructed. Applying these subspaces, an internal approximation of the dual problem for second order elliptic equations is defined. A convergence of this method is proved without any assumption of a regularity of the solution. For sufficiently smooth solutions an optimal rate of convergence is proved. The...