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We construct smoothed projections from Sobolev de\u00a0Rham complexes onto finite element de\u00a0Rham complexes which commute with the exterior derivative, preserve homogeneous boundary conditions along a fixed boundary part, and satisfy uniform bounds for shape-regular families of triangulations and bounded polynomial degree. The existence of such projections implies stability and quasi-optimal convergence of mixed finite element methods for the Hodge Laplace equation with mixed boundary conditions. In addition, we prove the density of smooth differential forms in Sobolev spaces of differential forms over weakly Lipschitz domains with partial boundary conditions.<\/p>","DOI":"10.1090\/mcom\/3330","type":"journal-article","created":{"date-parts":[[2017,10,18]],"date-time":"2017-10-18T09:30:32Z","timestamp":1508319032000},"page":"607-635","source":"Crossref","is-referenced-by-count":20,"title":["Smoothed projections and mixed boundary conditions"],"prefix":"10.1090","volume":"88","author":[{"given":"Martin","family":"Licht","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"14","published-online":{"date-parts":[[2018,4,10]]},"reference":[{"issue":"4","key":"1","doi-asserted-by":"publisher","first-page":"597","DOI":"10.1142\/S0218202503002672","article-title":"Unique solvability for electromagnetic boundary value problems in the presence of partly lossy inhomogeneous anisotropic media and mixed boundary conditions","volume":"13","author":"Alonso Rodr\u00edguez, Ana","year":"2003","journal-title":"Math. 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