On the approximation of electromagnetic fields by edge finite elements. Part 1: Sharp interpolation results for low-regularity fields - Archive ouverte HAL Access content directly
Journal Articles Computers & Mathematics with Applications Year : 2016

On the approximation of electromagnetic fields by edge finite elements. Part 1: Sharp interpolation results for low-regularity fields

Abstract

We propose sharp results on the numerical approximation of low-regularity electromagnetic fields by edge finite elements. We consider general geometrical settings, including topologically non-trivial domains or domains with a non-connected boundary. In the model, the electric permittivity and magnetic per-meability are symmetric, tensor-valued, piecewise smooth coefficients. In all cases, the error can be bounded by h δ times a constant, where h is the mesh-size, for some exponent δ ∈]0, 1] that depends both on the geometry and on the coefficients. It relies either on classical estimates when δ > 1/2, or on a new combined interpolation operator when δ < 1/2. The optimality of the value of δ is discussed with respect to abstract shift theorems. In some simple configurations , typically for scalar-valued permittivity and permeability, the value of δ can be further characterized. This paper is the first one in a series dealing with the approximation of electromagnetic fields by edge finite elements.
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Dates and versions

hal-01176476 , version 1 (28-05-2015)
hal-01176476 , version 2 (15-07-2015)
hal-01176476 , version 3 (01-10-2015)
hal-01176476 , version 4 (23-12-2015)

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Patrick Ciarlet. On the approximation of electromagnetic fields by edge finite elements. Part 1: Sharp interpolation results for low-regularity fields. Computers & Mathematics with Applications, 2016, ⟨10.1016/j.camwa.2015.10.020⟩. ⟨hal-01176476v4⟩
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