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Div-curl Lemma revisited: applications in electromagnetism. (English) Zbl 1201.78007

The authors establish two new time-dependent versions of div-curl results in a bounded domain \(\Omega\subset{\mathbb R}^3\). In the first part of this paper the main differences in compactness arguments for diffusion processes and for electromagnetic fields are shown. Next, some important versions of the div-curl lemma are recalled and new compactness results are proven. A numerical experiment from electromagnetic fields is presented in the final section of this paper.

MSC:

78A25 Electromagnetic theory (general)
65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
82D55 Statistical mechanics of superconductors
78M25 Numerical methods in optics (MSC2010)
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