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The results are based on Young measure theory and a weak\u2013strong stability estimate combining Shannon and Rao entropies. The convergence of the numerical scheme is achieved by means of discrete entropy dissipation inequalities and an artificial diffusion, which vanishes in the continuum limit.<\/jats:p>","DOI":"10.1007\/s00211-025-01474-7","type":"journal-article","created":{"date-parts":[[2025,5,16]],"date-time":"2025-05-16T10:49:25Z","timestamp":1747392565000},"page":"951-992","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Convergence of a finite-volume scheme and dissipative measure-valued\u2013strong stability for a hyperbolic\u2013parabolic cross-diffusion system"],"prefix":"10.1007","volume":"157","author":[{"given":"Katharina","family":"Hopf","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ansgar","family":"J\u00fcngel","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,5,16]]},"reference":[{"key":"1474_CR1","doi-asserted-by":"crossref","unstructured":"Amann, H.: Nonhomogeneous linear and quasilinear elliptic and parabolic boundary value problems. 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