{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:27:40Z","timestamp":1787333260392,"version":"build-2736575974"},"reference-count":43,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12071429"],"award-info":[{"award-number":["12071429"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12090020"],"award-info":[{"award-number":["12090020"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12272346"],"award-info":[{"award-number":["12272346"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2025,10,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>To numerically solve the two-dimensional advection equation, we propose a family of fourth- and higher-order semi-Lagrangian finite volume (SLFV) methods that feature (1) fourth-, sixth-, and eighth-order convergence rates, (2) applicability to both regular and irregular domains with arbitrarily complex topology and geometry, (3) ease of handling both zero and nonzero source terms, and (4) the same algorithmic steps for both periodic and incoming penetration conditions. Test results confirm the analysis and demonstrate the accuracy, flexibility, robustness, and excellent conditioning of the proposed SLFV method.<\/jats:p>","DOI":"10.1137\/24m171084x","type":"journal-article","created":{"date-parts":[[2025,9,26]],"date-time":"2025-09-26T07:28:26Z","timestamp":1758871706000},"page":"A2722-A2745","source":"Crossref","is-referenced-by-count":0,"title":["Fourth- and Higher-Order Semi-Lagrangian Finite Volume Methods for the Two-Dimensional Advection Equation on Arbitrarily Complex Domains"],"prefix":"10.1137","volume":"47","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-6808-4653","authenticated-orcid":true,"given":"Yunxia","family":"Sun","sequence":"first","affiliation":[{"name":"College of Mathematics and System Science, Xinjiang University, Urumqi, Xinjiang Province, 830046 China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6277-1407","authenticated-orcid":true,"given":"Kaiyi","family":"Liang","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Zhejiang University, Hangzhou, Zhejiang Province, 310058 China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuke","family":"Zhu","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Zhejiang University, Hangzhou, Zhejiang Province, 310058 China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-5829-3771","authenticated-orcid":true,"given":"Zhi","family":"Lin","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Zhejiang University, Hangzhou, Zhejiang Province, 310058 China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3655-4190","authenticated-orcid":true,"given":"Qinghai","family":"Zhang","sequence":"additional","affiliation":[{"name":"Corresponding author.\u00a0College of Mathematics and System Science, Xinjiang University, Urumqi, Xinjiang Province, 830046 China, and School of Mathematical Sciences, Zhejiang University, Hangzhou, Zhejiang Province, 310058 China."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2025,9,26]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1016\/j.matcom.2016.12.012"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1017\/S0022377899008065"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2015.02.014"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-07-01912-6"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-9991(03)00318-8"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1137\/050644549"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.4208\/cicp.OA-2020-0073"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2023.112329"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(84)90143-8"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1140\/epjd\/e2014-50180-9"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.2478\/v10006-007-0028-x"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2009.11.007"},{"key":"ref13","doi-asserted-by":"crossref","unstructured":"N. Crouseilles, M. Mehrenberger, and F. Vecil, A Discontinuous Galerkin Semi-Lagrangian Solver for the Guiding-Center Problem, 2012, https:\/\/inria.hal.science\/hal-00717155.","DOI":"10.1051\/proc\/2011022"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1137\/23M1559658"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2024.113574"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2012.01.030"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-9991(02)00079-7"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1996.0130"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2009.10.036"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1007\/s42967-021-00156-z"},{"key":"ref21","doi-asserted-by":"crossref","unstructured":"Y. Li, X. Wu, J. Yan, J. Yang, Q. Zhang, and S. Zhao, GePUP-ES: High-Order Energy-Stable Projection Methods for the Incompressible Navier-Stokes Equations with No-Slip Conditions, https:\/\/arxiv.org\/abs\/2409.11255, 2025.","DOI":"10.1007\/s10915-025-03087-6"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112007005332"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1175\/2009MWR2717.1"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2022.111589"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1016\/0771-050X(81)90010-3"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2009.10.016"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2010.04.037"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2011.07.018"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1080\/07055900.1981.9649098"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1137\/070679065"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.1017\/S0962492920000057"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1175\/1520-0469(1992)049<2082:ACOSLA>2.0.CO;2"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1998.6148"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1175\/1520-0493(1991)119<2206:SLISFA>2.0.CO;2"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1002\/9781119426479"},{"key":"ref36","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(85)90085-3"},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1137\/0715051"},{"key":"ref38","doi-asserted-by":"publisher","DOI":"10.1007\/s10915-018-0892-6"},{"key":"ref39","doi-asserted-by":"publisher","DOI":"10.1007\/s10915-015-0122-4"},{"key":"ref40","doi-asserted-by":"publisher","DOI":"10.1137\/17M1149328"},{"key":"ref41","doi-asserted-by":"publisher","DOI":"10.1090\/mcom\/3539"},{"key":"ref42","doi-asserted-by":"publisher","DOI":"10.1007\/s10915-024-02706-y"},{"key":"ref43","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2022.114973"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/24M171084X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:45:57Z","timestamp":1787330757000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/24M171084X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,9,26]]},"references-count":43,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2025,10,31]]}},"alternative-id":["10.1137\/24M171084X"],"URL":"https:\/\/doi.org\/10.1137\/24m171084x","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,9,26]]}}}