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The fracture geometry is parameterized by aperture functions on a submanifold of codimension one. Given a fracture, we derive the limit models as $  \\varepsilon \\rightarrow 0 $. Depending on the value of $ \\alpha $, we obtain five different limit models as $  \\varepsilon \\rightarrow 0 $, for which we present rigorous convergence results.&lt;\/p&gt;&lt;\/abstract&gt;<\/jats:p>","DOI":"10.3934\/nhm.2024006","type":"journal-article","created":{"date-parts":[[2024,1,31]],"date-time":"2024-01-31T06:47:30Z","timestamp":1706683650000},"page":"114-156","source":"Crossref","is-referenced-by-count":4,"title":["Rigorous derivation of discrete fracture models for Darcy flow in the limit of vanishing aperture"],"prefix":"10.3934","volume":"19","author":[{"given":"Maximilian","family":"H\u00f6rl","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Christian","family":"Rohde","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"2321","reference":[{"key":"key-10.3934\/nhm.2024006-1","doi-asserted-by":"publisher","unstructured":"S. Burbulla, M. H\u00f6rl, C. 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