{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,7]],"date-time":"2026-03-07T07:15:44Z","timestamp":1772867744733,"version":"3.50.1"},"reference-count":39,"publisher":"Walter de Gruyter GmbH","issue":"1","license":[{"start":{"date-parts":[[2025,6,26]],"date-time":"2025-06-26T00:00:00Z","timestamp":1750896000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,3,26]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>We investigate the consistency and convergence of flux-corrected finite element approximations in the context of nonlinear hyperbolic conservation laws. In particular, we focus on a monolithic convex limiting approach and prove a Lax\u2013Wendroff-type theorem for the corresponding semi-discrete problem. A key component of our analysis is the use of a weak estimate on bounded variation, which follows from the semi-discrete entropy stability property of the method under investigation. For the Euler equations of gas dynamics, we prove the weak convergence of the flux-corrected finite element scheme to a dissipative weak solution under the assumption that a gas stays in physically reasonable region, i.e., the density is uniformly bounded away from zero, and the energy is uniformly bounded from above. Furthermore, if a strong solution exists, the sequence of numerical approximations converges strongly to the strong solution.<\/jats:p>","DOI":"10.1515\/jnma-2024-0123","type":"journal-article","created":{"date-parts":[[2025,6,25]],"date-time":"2025-06-25T12:58:57Z","timestamp":1750856337000},"page":"1-20","source":"Crossref","is-referenced-by-count":0,"title":["Consistency and convergence of flux-corrected finite element methods for nonlinear hyperbolic problems"],"prefix":"10.1515","volume":"34","author":[{"given":"Dmitri","family":"Kuzmin","sequence":"first","affiliation":[{"name":"Institute of Applied Mathematics (LS III) , TU Dortmund University , Dortmund , Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M\u00e1ria","family":"Luk\u00e1\u010dov\u00e1-Medvid\u2019ov\u00e1","sequence":"additional","affiliation":[{"name":"Institute of Mathematics , Johannes Gutenberg University , Mainz , Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1367-1917","authenticated-orcid":false,"given":"Philipp","family":"\u00d6ffner","sequence":"additional","affiliation":[{"name":"Institute of Mathematics , Johannes Gutenberg University , Mainz , Germany"},{"name":"Institute of Mathematics , Clausthal University of Technology , Clausthal-Zellerfeld , Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2025,6,26]]},"reference":[{"key":"2026030615521530044_j_jnma-2024-0123_ref_001","doi-asserted-by":"crossref","unstructured":"C. Dafermos, Hyperbolic Conservation Laws in Continuum Physics, Grundlehren Math. Wiss, vol.\u00a0325, 3rd ed. Berlin, Springer-Verlag, 2010.","DOI":"10.1007\/978-3-642-04048-1_10"},{"key":"2026030615521530044_j_jnma-2024-0123_ref_002","doi-asserted-by":"crossref","unstructured":"G. Warnecke, Analytische Methoden in der Theorie der Erhaltungsgleichungen (Analytical Methods in the Theory of Conservation Laws), Stuttgart, Teubner, 1999.","DOI":"10.1007\/978-3-663-09264-3"},{"key":"2026030615521530044_j_jnma-2024-0123_ref_003","doi-asserted-by":"crossref","unstructured":"J. Smoller, Shock Waves and Reaction Diffusion Equations, New York, Springer, 1994.","DOI":"10.1007\/978-1-4612-0873-0"},{"key":"2026030615521530044_j_jnma-2024-0123_ref_004","unstructured":"R. Abgrall and C.-W. Shu, \u201cHandbook of numerical methods for hyperbolic problems: basic and fundamental issues,\u201d Handb. Numer. Anal., vol.\u00a017, 2016."},{"key":"2026030615521530044_j_jnma-2024-0123_ref_005","unstructured":"R. Abgrall and C.-W. Shu, \u201cHandbook of numerical methods for hyperbolic problems: applied and modern issues,\u201d Handb. Numer. Anal., vol.\u00a018, 2017."},{"key":"2026030615521530044_j_jnma-2024-0123_ref_006","doi-asserted-by":"crossref","unstructured":"J.-L. Guermond and B. Popov, \u201cInvariant domains and first-order continuous finite element approximation for hyperbolic systems,\u201d SIAM J. Numer. Anal., vol. 54, no. 4, pp. 2466\u20132489, 2016. https:\/\/doi.org\/10.1137\/16m1074291.","DOI":"10.1137\/16M1074291"},{"key":"2026030615521530044_j_jnma-2024-0123_ref_007","doi-asserted-by":"crossref","unstructured":"D. Kuzmin, M. M\u00f6ller, and M. Gurris, \u201cAlgebraic flux correction II. Compressible flow problems,\u201d in Flux-Corrected Transport: Principles, Algorithms, and Applications, 2nd ed D. Kuzmin, R. L\u00f6hner, and S. Turek, Eds., Dordrecht, Springer, 2012, pp. 193\u2013238.","DOI":"10.1007\/978-94-007-4038-9_7"},{"key":"2026030615521530044_j_jnma-2024-0123_ref_008","doi-asserted-by":"crossref","unstructured":"J.-L. Guermond, M. Nazarov, B. Popov, and I. Tomas, \u201cSecond-order invariant domain preserving approximation of the Euler equations using convex limiting,\u201d SIAM J. Sci. Comput., vol. 40, no. 5, pp. A3211\u2013A3239, 2018. https:\/\/doi.org\/10.1137\/17m1149961.","DOI":"10.1137\/17M1149961"},{"key":"2026030615521530044_j_jnma-2024-0123_ref_009","doi-asserted-by":"crossref","unstructured":"D. Kuzmin, \u201cMonolithic convex limiting for continuous finite element discretizations of hyperbolic conservation laws,\u201d Comput. Methods Appl. Mech. Eng., vol.\u00a0361, p.\u00a0112804, 2020, https:\/\/doi.org\/10.1016\/j.cma.2019.112804.","DOI":"10.1016\/j.cma.2019.112804"},{"key":"2026030615521530044_j_jnma-2024-0123_ref_010","doi-asserted-by":"crossref","unstructured":"D. Kuzmin and M. 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