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A wavenumber-explicit stability and regularity theory is developed that decomposes the solution into a part with finite Sobolev regularity that is controlled uniformly in <jats:italic>k<\/jats:italic> and an analytic part. Using this regularity, quasi-optimality of the Galerkin discretization based on N\u00e9d\u00e9lec elements of order <jats:italic>p<\/jats:italic> on a mesh with mesh size <jats:italic>h<\/jats:italic> is shown under the <jats:italic>k<\/jats:italic>-explicit scale resolution condition that (a) <jats:italic>kh<\/jats:italic>\/<jats:italic>p<\/jats:italic> is sufficient small and (b) <jats:inline-formula><jats:alternatives><jats:tex-math>$$p\/\\ln k$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>p<\/mml:mi>\n                    <mml:mo>\/<\/mml:mo>\n                    <mml:mo>ln<\/mml:mo>\n                    <mml:mi>k<\/mml:mi>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> is bounded from below.<\/jats:p>","DOI":"10.1007\/s10208-023-09626-7","type":"journal-article","created":{"date-parts":[[2023,11,14]],"date-time":"2023-11-14T15:02:29Z","timestamp":1699974149000},"page":"1871-1939","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Wavenumber-Explicit hp-FEM Analysis for Maxwell\u2019s Equations with Impedance Boundary Conditions"],"prefix":"10.1007","volume":"24","author":[{"given":"J. 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