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Mixed discontinuous Galerkin approximation of the Maxwell operator: non-stabilized formulation. (English) Zbl 1091.78017

The authors propose in this paper a mixed discontinuous Galerkin finite element method for the discretization of the Maxwell operator on simplicial meshes. The main feature consists in the presence of mixed-order finite element spaces for the approximation of the unknowns and the choice of such spaces eliminates the need to penalize the normal jumps in the approximation to the vector unknown. Numerical experiments provided by the authors show that this method is also optimally convergent when the error is measured in terms of the \(L^2\)-norm.

MSC:

78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory
65Z05 Applications to the sciences
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References:

[9] Houston, P., Perugia, I., and Schötzau, D. (2004). Nonconforming Mixed Finite Element Approximations to Time-Harmonic Eddy Current Problems. Technical Report 2003/15, University of Leicester, Department of Mathematics. IEEE Trans. Mag. 40, 1268–1273.
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