Maxwell’s Equations : Analysis and Numerics

This volume collects longer articles on the analysis and numerics of Maxwell’s equations. The topics include functional analytic and Hilbert space methods, compact embeddings, solution theories and asymptotics, electromagnetostatics, time-harmonic Maxwell’s equations, time-dependent Maxwell’s equations, eddy current approximations, scattering and radiation problems, inverse problems, finite element methods, boundary element methods, and isogeometric analysis. * A collection of original survey articles on Maxwell's equations * Both analytical as well as computational approaches are presented * Of interest to applied mathematicians, but also to physicists and engineers working in electromagnetism Preface Contents 1. The curl–div system: theory and finite element approximation 2. Darwin and higher order approximations to Maxwell’s equations in R 3 3. Weck’s selection theorem: The Maxwell compactness property for bounded weak Lipschitz domains with mixed boundary conditions in arbitrary dimensions 4. Numerical analysis of the half-space matching method with Robin traces on a convex polygonal scatterer 5. Eigenvalue problems in inverse electromagnetic scattering theory 6. Maxwell eigenmodes in product domains 7. Discrete regular decompositions of tetrahedral discrete 1-forms 8. Some old and some new results in inverse obstacle scattering 9. The time-harmonic Maxwell equations with impedance boundary conditions in polyhedral domains 10. Time-harmonic electro-magnetic scattering in exterior weak Lipschitz domains with mixed boundary conditions 11. On an electro-magneto-elasto-dynamic transmission problem 12. Continuous dependence on the coefficients for a class of non-autonomous evolutionary equations