{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,17]],"date-time":"2025-11-17T21:42:39Z","timestamp":1763415759664,"version":"3.40.4"},"reference-count":21,"publisher":"Walter de Gruyter GmbH","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,3,28]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>We present a loosely coupled, non-iterative time-splitting scheme based on Robin\u2013Robin coupling conditions. We apply a novel unified analysis for this scheme applied to both a parabolic\/parabolic coupled system and a parabolic\/hyperbolic coupled system. We show for both systems that the scheme is stable, and the error converges as <jats:inline-formula>\n                     <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_jnma-2021-0119_eq_001.png\"\/>\n                        \n                        <jats:tex-math>$\\mathcal{O}\\big({\\Delta t} \\sqrt{T +\\log(\\frac{1}{{\\Delta t}})}\\big),$<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula>where <jats:italic>\u0394t<\/jats:italic> is the time step.<\/jats:p>","DOI":"10.1515\/jnma-2021-0119","type":"journal-article","created":{"date-parts":[[2025,4,16]],"date-time":"2025-04-16T10:08:19Z","timestamp":1744798099000},"page":"59-77","source":"Crossref","is-referenced-by-count":6,"title":["Loosely coupled, non-iterative time-splitting scheme based on Robin\u2013Robin coupling: Unified analysis for parabolic\/parabolic and parabolic\/hyperbolic problems"],"prefix":"10.1515","volume":"31","author":[{"given":"Erik","family":"Burman","sequence":"first","affiliation":[{"name":"Department of Mathematics, University College London , Gower street , London WC1E 6BT , United Kingdom"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rebecca","family":"Durst","sequence":"additional","affiliation":[{"name":"Division of Applied Mathematics, Brown University , 182 George street, Providence , Rhode Island , US ."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Miguel","family":"Fern\u00e1ndez","sequence":"additional","affiliation":[{"name":"Inst. Natl. Rech. Informat. and Automat. , BP 105, 78153 Le Chesnay , France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Johnny","family":"Guzm\u00e1n","sequence":"additional","affiliation":[{"name":"Division of Applied Mathematics, Brown University , 182 George street, Providence , Rhode Island , US ."}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2022,6,25]]},"reference":[{"key":"2025041610023126988_j_jnma-2021-0119_ref_001","unstructured":"M. S. Alnaes, J. Blechta, J. Hake, A. Johansson, B. Kehlet, A. Logg, C. Richardson, J. Ring, M. E. Rognes, and G. N. Wells, The FEniCS Project Version 1.5, Archive of Numerical Software 3 (2015)."},{"key":"2025041610023126988_j_jnma-2021-0119_ref_002","doi-asserted-by":"crossref","unstructured":"S. Badia, F. Nobile, and C. Vergara, Fluid\u2013structure partitioned procedures based on Robin transmission conditions, J. Comput. 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