{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:41:06Z","timestamp":1787330466443,"version":"build-2736575974"},"reference-count":30,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","funder":[{"DOI":"10.13039\/100000181","name":"Air Force Office of Scientific Research","doi-asserted-by":"publisher","award":["F49550-12-1-0399"],"award-info":[{"award-number":["F49550-12-1-0399"]}],"id":[{"id":"10.13039\/100000181","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11471305"],"award-info":[{"award-number":["11471305"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-1418750"],"award-info":[{"award-number":["DMS-1418750"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2017,1]]},"abstract":"<jats:p>In this paper, we develop and analyze the Runge--Kutta discontinuous Galerkin (RKDG) method to solve weakly coupled hyperbolic multidomain problems. Such problems involve transfer type boundary conditions with discontinuous fluxes between different domains, calling for special techniques to prove stability of the RKDG methods. We prove both stability and error estimates for our RKDG methods on simple models, and then apply them to a biological cell proliferation model [N. Echenim, D. Monniaux, M. Sorine, and F. Cl\u00e9ment, Math. Biosci., 198 (2005), pp. 57--79]. Numerical results are provided to illustrate the good behavior of our RKDG methods.<\/jats:p>","DOI":"10.1137\/16m1089332","type":"journal-article","created":{"date-parts":[[2017,9,26]],"date-time":"2017-09-26T14:12:18Z","timestamp":1506435138000},"page":"A2201-A2230","source":"Crossref","is-referenced-by-count":0,"title":["Discontinuous Galerkin Methods for Weakly Coupled Hyperbolic MultiDomain Problems"],"prefix":"10.1137","volume":"39","author":[{"given":"Qingyuan","family":"Liu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chi-Wang","family":"Shu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mengping","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2017,9,26]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1051\/proc\/201238006"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1137\/120904238"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1137\/120865768"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1007\/s10665-008-9213-7"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2005.08.019"},{"key":"atypb6","first-page":"455","volume-title":"Proc. Sympos. Appl. Math. 67","author":"B\u00fcrger R.","year":"2009"},{"key":"atypb7","first-page":"545","volume":"54","author":"Cockburn B.","year":"1990","journal-title":"Math. Comp."},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142900371544"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(89)90183-6"},{"key":"atypb10","first-page":"411","volume":"52","author":"Cockburn B.","year":"1989","journal-title":"Math. Comput."},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1998.5892"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1023\/A:1012873910884"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898719208"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1051\/proc\/2009028"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1016\/j.pbiomolbio.2012.12.005"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1137\/080737472"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1137\/060664495"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1016\/j.mbs.2005.05.003"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1137\/S003614450036757X"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1007\/s11425-013-4739-1"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1152\/physrev.1980.60.1.51"},{"key":"atypb22","unstructured":"W. H. Reed and T. R. Hill,\n                      Triangular Mesh Methods for the Neutron Transport Equation\n                      , Report LA-UR-73-479, Los Alamos Scientific Laboratory, 1973."},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1142\/S0218202503002477"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2013.01.001"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(88)90177-5"},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1016\/j.cub.2008.07.001"},{"key":"atypb27","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142902404182"},{"key":"atypb28","doi-asserted-by":"publisher","DOI":"10.1137\/090771363"},{"key":"atypb29","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2009.12.030"},{"key":"atypb30","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2011.11.020"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/16M1089332","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:06:55Z","timestamp":1787328415000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/16M1089332"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,1]]},"references-count":30,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2017,1]]}},"alternative-id":["10.1137\/16M1089332"],"URL":"https:\/\/doi.org\/10.1137\/16m1089332","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,1]]}}}