Chapter 8 Curl-conforming Edge Element Methods 8.1 Maxwell's Equations 8.1.1 Introduction

Electromagnetic phenomena can be described by the electric field E, the electric induction D, the current density J as well as the magnetic field H and the magnetic induction B according to Maxwell's equations given by Faraday's law ∂B ∂t + curl E = 0 in lR 3 , (8.1) where according to the Gauss law div B = 0 in lR 3 , (8.2) and Ampère's law ∂D ∂t − curl H + J = 0 in lR 3 , (8.3) where, again observing the Gauss law div D = ρ in lR 3. (8.4) Figure 8.1: Faraday's law In particular, Faraday's law describes how an electric field can be induced by a changing magnetic flux. It states that the induced electric field is proportional to the time rate of change of the magnetic flux through the circuit. For D ⊂ lR 3 the integral form of Faraday's law states: D ∂B ∂t dx = − ∂D E ∧ n dσ ,