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This monograph covers the mathematical theory and tools behind electromagnetism – governed by Maxwell’s equations. After some background in functional analysis is introduced, the spectral theory of the Maxwell operator is discussed. Results available for special limits and decompositions, such as static and time-harmonic are taken into consideration as well as error estimates relevant when solving those equations.
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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.