{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T13:23:02Z","timestamp":1767964982173,"version":"3.49.0"},"reference-count":22,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2019,6,20]],"date-time":"2019-06-20T00:00:00Z","timestamp":1560988800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2019,6,20]],"date-time":"2019-06-20T00:00:00Z","timestamp":1560988800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"DFG","award":["HE4858\/4-1"],"award-info":[{"award-number":["HE4858\/4-1"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2019,9]]},"DOI":"10.1007\/s10915-019-00988-1","type":"journal-article","created":{"date-parts":[[2019,6,20]],"date-time":"2019-06-20T07:24:17Z","timestamp":1561015457000},"page":"1463-1497","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":26,"title":["A New ADER Method Inspired by the Active Flux Method"],"prefix":"10.1007","volume":"80","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9901-7149","authenticated-orcid":false,"given":"Christiane","family":"Helzel","sequence":"first","affiliation":[]},{"given":"David","family":"Kerkmann","sequence":"additional","affiliation":[]},{"given":"Leonardo","family":"Scandurra","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2019,6,20]]},"reference":[{"key":"988_CR1","doi-asserted-by":"crossref","unstructured":"Barsukow, W., Hohm, J., Klingenberg, C., Roe, P.L.: The active flux scheme on Cartesian grids and its low mach number limit (2018)","DOI":"10.1007\/s10915-019-01031-z"},{"key":"988_CR2","doi-asserted-by":"crossref","unstructured":"Eymann, T.A., Roe, P.L.: Active flux schemes. AIAA 2011-382","DOI":"10.2514\/6.2011-382"},{"key":"988_CR3","doi-asserted-by":"crossref","unstructured":"Eymann, T.A., Roe, P.L.: Active flux schemes for systems. AIAA 2011-3840","DOI":"10.2514\/6.2011-3840"},{"key":"988_CR4","doi-asserted-by":"crossref","unstructured":"Eymann, T.A., Roe, P.L.: Multidimensional active flux schemes. In: AIAA Conference Paper (2013)","DOI":"10.2514\/6.2013-2940"},{"key":"988_CR5","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611975109","volume-title":"Numerical Methods for Conservation Laws: From Analysis to Algorithm (Computational Science and Engineering)","author":"JS Hesthaven","year":"2018","unstructured":"Hesthaven, J.S.: Numerical Methods for Conservation Laws: From Analysis to Algorithm (Computational Science and Engineering). SIAM, Philadelphia (2018)"},{"key":"988_CR6","doi-asserted-by":"publisher","first-page":"1390","DOI":"10.1007\/s10915-016-0286-6","volume":"70","author":"K Kaiser","year":"2017","unstructured":"Kaiser, K., Sch\u00fctz, J., Sch\u00f6bel, R., Noelle, S.: A new stable splitting for the isentropic Euler equations. J. Sci. Comput. 70, 1390\u20131407 (2017)","journal-title":"J. Sci. Comput."},{"key":"988_CR7","doi-asserted-by":"publisher","first-page":"7426","DOI":"10.1016\/j.jcp.2009.06.037","volume":"228","author":"SA Karabasov","year":"2009","unstructured":"Karabasov, S.A., Goloviznin, V.M.: Compact accurately boundary-adjusting high-resolution technique for fluid dynamics. J. Comput. Phys. 228, 7426\u20137451 (2009)","journal-title":"J. Comput. Phys."},{"key":"988_CR8","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511791253","volume-title":"Finite Volume Methods for Hyperbolic Problems","author":"RJ LeVeque","year":"2002","unstructured":"LeVeque, R.J.: Finite Volume Methods for Hyperbolic Problems. Cambridge University Press, Cambridge (2002)"},{"key":"988_CR9","doi-asserted-by":"publisher","first-page":"1355","DOI":"10.1090\/S0025-5718-00-01228-X","volume":"69","author":"M Luk\u00e1\u010dov\u00e1-Medvid\u2019ov\u00e1","year":"2000","unstructured":"Luk\u00e1\u010dov\u00e1-Medvid\u2019ov\u00e1, M., Morton, K.W., Warnecke, G.: Evolution Galerkin methods for hyperbolic systems in two space dimensions. Math. Comput. 69, 1355\u20131384 (2000)","journal-title":"Math. Comput."},{"key":"988_CR10","doi-asserted-by":"publisher","first-page":"892","DOI":"10.1137\/0915054","volume":"15","author":"A Marquina","year":"1994","unstructured":"Marquina, A.: Local piecewise hyperbolic reconstruction of numerical fluxes for nonlinear scalar conservation laws. SIAM J. Sci. Comput. 15, 892\u2013915 (1994)","journal-title":"SIAM J. Sci. Comput."},{"key":"988_CR11","doi-asserted-by":"publisher","first-page":"905","DOI":"10.4208\/cicp.OA-2016-0052","volume":"21","author":"P Roe","year":"2017","unstructured":"Roe, P.: A simple explanation of superconvergence for discontinuous Galerkin solutions to $$u_t + u_x = 0$$. Commun. Comput. Phys. 21, 905\u2013912 (2017)","journal-title":"Commun. Comput. Phys."},{"key":"988_CR12","doi-asserted-by":"publisher","first-page":"1094","DOI":"10.1007\/s10915-017-0555-z","volume":"73","author":"P Roe","year":"2017","unstructured":"Roe, P.: Is discontinuous reconstruction really a good idea? J. Sci. Comput. 73, 1094\u20131114 (2017)","journal-title":"J. Sci. Comput."},{"key":"988_CR13","doi-asserted-by":"crossref","unstructured":"Roe, P.L., Lung, T., Maeng, J.: New approaches to limiting. In: 22nd AIAA Computational Fluid Dynamics Conference (2015)","DOI":"10.2514\/6.2015-2913"},{"key":"988_CR14","doi-asserted-by":"crossref","unstructured":"Roe, P.L., Maeng, J., Fan, D.: Comparing active flux and discontinuous Galerkin methods for compressible flow. In: 2018 AIAA Aerospace Science Meeting (2018)","DOI":"10.2514\/6.2018-0836"},{"key":"988_CR15","doi-asserted-by":"publisher","first-page":"82","DOI":"10.1137\/070679065","volume":"51","author":"C-W Shu","year":"2009","unstructured":"Shu, C.-W.: High order weighted essentially nonoscillatory schemes for convection dominated problems. SIAM Rev. 51, 82\u2013126 (2009)","journal-title":"SIAM Rev."},{"key":"988_CR16","doi-asserted-by":"publisher","first-page":"32","DOI":"10.1016\/0021-9991(89)90222-2","volume":"83","author":"C-W Shu","year":"1989","unstructured":"Shu, C.-W., Osher, S.: Efficient implementation of essentially non-oscillarory shock-capturing schemes, II. J. Comput. Phys. 83, 32\u201378 (1989)","journal-title":"J. Comput. Phys."},{"key":"988_CR17","doi-asserted-by":"publisher","first-page":"609","DOI":"10.1023\/A:1015126814947","volume":"17","author":"VA Titarev","year":"2002","unstructured":"Titarev, V.A., Toro, E.F.: ADER: arbitrary high order Godunov approach. J. Sci. Comput. 17, 609\u2013618 (2002)","journal-title":"J. Sci. Comput."},{"key":"988_CR18","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.compfluid.2012.08.023","volume":"70","author":"EF Toro","year":"2012","unstructured":"Toro, E.F., V\u00e1zquez-Cend\u00f3n, M.E.: Flux splitting schemes for the Euler equations. Comput. Fluids 70, 1\u201312 (2012)","journal-title":"Comput. Fluids"},{"key":"988_CR19","volume-title":"Numerical Solution of Hyperbolic Partial Differential Equations","author":"JA Trangenstein","year":"2009","unstructured":"Trangenstein, J.A.: Numerical Solution of Hyperbolic Partial Differential Equations. Cambridge University Press, Cambridge (2009)"},{"key":"988_CR20","doi-asserted-by":"publisher","first-page":"276","DOI":"10.1016\/0021-9991(77)90095-X","volume":"23","author":"B van Leer","year":"1977","unstructured":"van Leer, B.: Towards the ultimate conservative difference scheme. IV. A new approach to numerical convection. J. Comput. Phys. 23, 276\u2013299 (1977)","journal-title":"J. Comput. Phys."},{"key":"988_CR21","doi-asserted-by":"publisher","first-page":"91","DOI":"10.1016\/j.compfluid.2014.02.007","volume":"98","author":"X Zeng","year":"2014","unstructured":"Zeng, X.: A high-order hybrid finite difference\u2013finite volume approach with application to inviscid compressible flow problems: a preliminary study. Comput. Fluids 98, 91\u2013110 (2014)","journal-title":"Comput. Fluids"},{"key":"988_CR22","doi-asserted-by":"publisher","first-page":"2752","DOI":"10.1098\/rspa.2011.0153","volume":"467","author":"X Zhang","year":"2011","unstructured":"Zhang, X., Shu, C.-W.: Maximum-principle-satisfying and positivity-preserving high-order schemes for conservation laws: survey and new developments. Proc. R. Soc. A 467, 2752\u20132776 (2011)","journal-title":"Proc. R. Soc. A"}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-019-00988-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-019-00988-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-019-00988-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,6,18]],"date-time":"2020-06-18T23:07:54Z","timestamp":1592521674000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-019-00988-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,6,20]]},"references-count":22,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2019,9]]}},"alternative-id":["988"],"URL":"https:\/\/doi.org\/10.1007\/s10915-019-00988-1","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,6,20]]},"assertion":[{"value":"16 April 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 May 2019","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 June 2019","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 June 2019","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}