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We show that Maubach\u2019s routine with this initialization always terminates and generates meshes that preserve shape regularity and satisfy the closure estimate needed for optimal convergence of adaptive schemes. Our ansatz allows for the intrinsic use of existing implementations.<\/jats:p>","DOI":"10.1007\/s10208-025-09698-7","type":"journal-article","created":{"date-parts":[[2025,3,27]],"date-time":"2025-03-27T00:21:59Z","timestamp":1743034919000},"page":"1193-1218","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Adaptive Mesh Refinement for Arbitrary Initial Triangulations"],"prefix":"10.1007","volume":"26","author":[{"given":"Lars","family":"Diening","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lukas","family":"Gehring","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Johannes","family":"Storn","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,3,24]]},"reference":[{"key":"9698_CR1","doi-asserted-by":"publisher","unstructured":"M. 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