{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,18]],"date-time":"2026-04-18T05:10:32Z","timestamp":1776489032995,"version":"3.51.2"},"reference-count":44,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2022,8,1]],"date-time":"2022-08-01T00:00:00Z","timestamp":1659312000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,8,1]],"date-time":"2022-08-01T00:00:00Z","timestamp":1659312000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100004052","name":"King Abdullah University of Science and Technology","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100004052","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2022,9]]},"DOI":"10.1007\/s10915-022-01922-8","type":"journal-article","created":{"date-parts":[[2022,8,1]],"date-time":"2022-08-01T09:08:27Z","timestamp":1659344907000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Maximum Principle Preserving Space and Time Flux Limiting for Diagonally Implicit Runge\u2013Kutta Discretizations of Scalar Convection-diffusion Equations"],"prefix":"10.1007","volume":"92","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9431-6481","authenticated-orcid":false,"given":"Manuel","family":"Quezada de Luna","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1212-126X","authenticated-orcid":false,"given":"David I.","family":"Ketcheson","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,8,1]]},"reference":[{"key":"1922_CR1","doi-asserted-by":"publisher","first-page":"102","DOI":"10.1016\/j.jcp.2016.12.031","volume":"334","author":"R Anderson","year":"2017","unstructured":"Anderson, R., Dobrev, V., Kolev, T., Kuzmin, D., de Luna, M.Q., Rieben, R., Tomov, V.: High-order local maximum principle preserving (MPP) discontinuous Galerkin finite element method for the transport equation. J. Comput. Phys. 334, 102\u2013124 (2017)","journal-title":"J. Comput. Phys."},{"key":"1922_CR2","doi-asserted-by":"publisher","first-page":"113155","DOI":"10.1016\/j.cma.2020.113155","volume":"368","author":"T Arbogast","year":"2020","unstructured":"Arbogast, T., Huang, C.-S., Zhao, X., King, D.N.: A third order, implicit, finite volume, adaptive Runge\u2013Kutta WENO scheme for advection\u2013diffusion equations. Comput. Methods Appl. Mech. Eng. 368, 113155 (2020)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"3","key":"1922_CR3","doi-asserted-by":"publisher","first-page":"237","DOI":"10.1051\/m2an\/1978120302371","volume":"12","author":"C Bolley","year":"1978","unstructured":"Bolley, C., Crouzeix, M.: Conservation de la positivit\u00e9 lors de la discr\u00e9tisation des probl\u00e9mes d\u2019\u00e9volution paraboliques. R.A.I.R.O. Anal. Num\u00e9rique 12(3), 237\u2013245 (1978)","journal-title":"R.A.I.R.O. Anal. Num\u00e9rique"},{"issue":"1","key":"1922_CR4","doi-asserted-by":"publisher","first-page":"38","DOI":"10.1016\/0021-9991(73)90147-2","volume":"11","author":"JP Boris","year":"1973","unstructured":"Boris, J.P., Book, D.L.: Flux-corrected transport. I. SHASTA, a fluid transport algorithm that works. J. Comput. Phys. 11(1), 38\u201369 (1973)","journal-title":"J. Comput. Phys."},{"key":"1922_CR5","doi-asserted-by":"publisher","first-page":"198","DOI":"10.1016\/j.jcp.2015.12.039","volume":"308","author":"Z Chen","year":"2016","unstructured":"Chen, Z., Huang, H., Yan, J.: Third order maximum-principle-satisfying direct discontinuous Galerkin methods for time dependent convection diffusion equations on unstructured triangular meshes. J. Comput. Phys. 308, 198\u2013217 (2016)","journal-title":"J. Comput. Phys."},{"key":"1922_CR6","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1016\/j.jcp.2019.06.053","volume":"396","author":"D Feng","year":"2019","unstructured":"Feng, D., Neuweiler, I., Nackenhorst, U., Wick, T.: A time-space flux-corrected transport finite element formulation for solving multi-dimensional advection-diffusion-reaction equations. J. Comput. Phys. 396, 31\u201353 (2019)","journal-title":"J. Comput. Phys."},{"key":"1922_CR7","doi-asserted-by":"crossref","unstructured":"Gottlieb, S., Ketcheson, D.I., Shu, C.-W.: Strong Stability Preserving Runge-Kutta And Multistep Time Discretizations. WORLD SCIENTIFIC, (2011)","DOI":"10.1142\/7498"},{"issue":"4","key":"1922_CR8","doi-asserted-by":"publisher","first-page":"2163","DOI":"10.1137\/130950240","volume":"52","author":"J-L Guermond","year":"2014","unstructured":"Guermond, J.-L., Nazarov, M., Popov, B., Yang, Y.: A second-order maximum principle preserving lagrange finite element technique for nonlinear scalar conservation equations. SIAM J. Numer. Anal. 52(4), 2163\u20132182 (2014)","journal-title":"SIAM J. Numer. Anal."},{"issue":"4","key":"1922_CR9","doi-asserted-by":"publisher","first-page":"2466","DOI":"10.1137\/16M1074291","volume":"54","author":"J-L Guermond","year":"2016","unstructured":"Guermond, J.-L., Popov, B.: Invariant domains and first-order continuous finite element approximation for hyperbolic systems. SIAM J. Numer. Anal. 54(4), 2466\u20132489 (2016)","journal-title":"SIAM J. Numer. Anal."},{"key":"1922_CR10","series-title":"Springer Series in Computational Mathematics","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-05221-7","volume-title":"Solving ordinary differential equations II: Stiff and differential-algebraic problems","author":"E Hairer","year":"1996","unstructured":"Hairer, E., Wanner, G.: Solving ordinary differential equations II: Stiff and differential-algebraic problems. Springer Series in Computational Mathematics, vol. 14, 2nd edn. Springer, Berlin (1996)","edition":"2"},{"key":"1922_CR11","doi-asserted-by":"publisher","first-page":"120","DOI":"10.1016\/j.camwa.2021.02.012","volume":"87","author":"H Hajduk","year":"2021","unstructured":"Hajduk, H.: Monolithic convex limiting in discontinuous Galerkin discretizations of hyperbolic conservation laws. Comput. Math. Appl. 87, 120\u2013138 (2021)","journal-title":"Comput. Math. Appl."},{"issue":"3","key":"1922_CR12","doi-asserted-by":"publisher","first-page":"568","DOI":"10.1016\/0021-9991(72)90012-5","volume":"9","author":"A Harten","year":"1972","unstructured":"Harten, A., Zwas, G.: Self-adjusting hybrid schemes for shock computations. J. Comput. Phys. 9(3), 568\u2013583 (1972)","journal-title":"J. Comput. Phys."},{"issue":"2","key":"1922_CR13","doi-asserted-by":"publisher","first-page":"260","DOI":"10.1006\/jcph.1997.5713","volume":"135","author":"A Harten","year":"1997","unstructured":"Harten, A.: High resolution schemes for hyperbolic conservation laws. J. Comput. Phys. 135(2), 260\u2013278 (1997)","journal-title":"J. Comput. Phys."},{"key":"1922_CR14","doi-asserted-by":"crossref","unstructured":"Harten, A.: Method of artificial compression. I. shocks and contact discontinuities. Technical report, New York Univ., NY (USA). AEC Computing and Applied Mathematics Center, (1974)","DOI":"10.2172\/4300016"},{"issue":"2\u20134","key":"1922_CR15","doi-asserted-by":"publisher","first-page":"309","DOI":"10.1016\/S0168-9274(98)00050-6","volume":"28","author":"Z Horv\u00e1th","year":"1998","unstructured":"Horv\u00e1th, Z.: Positivity of Runge-Kutta and diagonally split Runge-Kutta methods. Appl. Numer. Math. 28(2\u20134), 309\u2013326 (1998)","journal-title":"Appl. Numer. Math."},{"issue":"5","key":"1922_CR16","doi-asserted-by":"publisher","first-page":"383","DOI":"10.1016\/0168-9274(93)90096-A","volume":"13","author":"A Jameson","year":"1993","unstructured":"Jameson, A.: Computational algorithms for aerodynamic analysis and design. Appl. Numer. Math. 13(5), 383\u2013422 (1993)","journal-title":"Appl. Numer. Math."},{"issue":"1","key":"1922_CR17","doi-asserted-by":"publisher","first-page":"202","DOI":"10.1006\/jcph.1996.0130","volume":"126","author":"G-S Jiang","year":"1996","unstructured":"Jiang, G.-S., Shu, C.-W.: Efficient implementation of weighted ENO schemes. J. Comput. Phys. 126(1), 202\u2013228 (1996)","journal-title":"J. Comput. Phys."},{"key":"1922_CR18","unstructured":"Kennedy, C.A., Carpenter, M.H.: Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations, a Review. National Aeronautics and Space Administration, Langley Research Center (2016)"},{"issue":"2","key":"1922_CR19","doi-asserted-by":"publisher","first-page":"175","DOI":"10.2140\/camcos.2014.9.175","volume":"9","author":"DI Ketcheson","year":"2014","unstructured":"Ketcheson, D.I., bin Waheed, U.: A comparison of high order explicit Runge-Kutta, extrapolation, and deferred correction methods in serial and parallel. CAMCoS 9(2), 175\u2013200 (2014)","journal-title":"CAMCoS"},{"issue":"6","key":"1922_CR20","doi-asserted-by":"publisher","first-page":"2381","DOI":"10.1137\/040614189","volume":"29","author":"A Kurganov","year":"2007","unstructured":"Kurganov, A., Petrova, G., Popov, B.: Adaptive semidiscrete central-upwind schemes for nonconvex hyperbolic conservation laws. SIAM J. Scientific Comput. 29(6), 2381\u20132401 (2007)","journal-title":"SIAM J. Scientific Comput."},{"key":"1922_CR21","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2019.112804","volume":"361","author":"D Kuzmin","year":"2020","unstructured":"Kuzmin, D.: Monolithic convex limiting for continuous finite element discretizations of hyperbolic conservation laws. Comput. Methods Appl. Mech. Eng. 361, 112804 (2020)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"1922_CR22","doi-asserted-by":"crossref","unstructured":"Kuzmin, Dmitri, de Luna, Manuel Quezada: Algebraic entropy fixes and convex limiting for continuous finite element discretizations of scalar hyperbolic conservation laws. Comput. Methods Appl. Mech. Eng. 372, 113370 (2020)","DOI":"10.1016\/j.cma.2020.113370"},{"key":"1922_CR23","doi-asserted-by":"publisher","DOI":"10.1016\/j.compfluid.2020.104742","volume":"213","author":"D Kuzmin","year":"2020","unstructured":"Kuzmin, D., de Luna, M.Q.: Entropy conservation property and entropy stabilization of high-order continuous Galerkin approximations to scalar conservation laws. Comput. Fluids 213, 104742 (2020)","journal-title":"Comput. Fluids"},{"key":"1922_CR24","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2020.109411","volume":"411","author":"D Kuzmin","year":"2020","unstructured":"Kuzmin, D., de Luna, M.Q.: Subcell flux limiting for high-order Bernstein finite element discretizations of scalar hyperbolic conservation laws. J. Comput. Phys. 411, 109411 (2020)","journal-title":"J. Comput. Phys."},{"key":"1922_CR25","unstructured":"Kuzmin, D., de\u00a0Luna, M.Q., Ketcheson, D.I., Gr\u00fcll, J.: Bound-preserving convex limiting for high-order Runge-Kutta time discretizations of hyperbolic conservation laws. arXiv:2009.01133, (2020)"},{"key":"1922_CR26","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-007-4038-9","volume-title":"Flux-corrected transport: principles, algorithms, and applications","author":"D Kuzmin","year":"2012","unstructured":"Kuzmin, D., L\u00f6hner, R., Turek, S.: Flux-corrected transport: principles, algorithms, and applications. Springer, Berlin (2012)"},{"issue":"24","key":"1922_CR27","doi-asserted-by":"publisher","first-page":"9284","DOI":"10.1016\/j.jcp.2010.08.039","volume":"229","author":"J-L Lee","year":"2010","unstructured":"Lee, J.-L., Bleck, R., MacDonald, A.E.: A multistep flux-corrected transport scheme. J. Comput. Phys. 229(24), 9284\u20139298 (2010)","journal-title":"J. Comput. Phys."},{"key":"1922_CR28","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-8629-1","volume-title":"Numerical methods for conservation laws","author":"RJ LeVeque","year":"1992","unstructured":"LeVeque, R.J.: Numerical methods for conservation laws, vol. 132. Springer, Berlin (1992)"},{"issue":"2","key":"1922_CR29","doi-asserted-by":"publisher","first-page":"627","DOI":"10.1137\/0733033","volume":"33","author":"RJ Leveque","year":"1996","unstructured":"Leveque, R.J.: High-resolution conservative algorithms for advection in incompressible flow. SIAM J. Numer. Anal. 33(2), 627\u2013665 (1996)","journal-title":"SIAM J. Numer. Anal."},{"key":"1922_CR30","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, vol. 31. Cambridge University Press, Cambridge (2002)"},{"issue":"1","key":"1922_CR31","doi-asserted-by":"publisher","first-page":"200","DOI":"10.1006\/jcph.1994.1187","volume":"115","author":"X-D Liu","year":"1994","unstructured":"Liu, X.-D., Osher, S., Chan, T.: Weighted essentially non-oscillatory schemes. J. Comput. Phys. 115(1), 200\u2013212 (1994)","journal-title":"J. Comput. Phys."},{"key":"1922_CR32","doi-asserted-by":"publisher","first-page":"151","DOI":"10.1016\/j.jcp.2017.04.059","volume":"344","author":"C Lohmann","year":"2017","unstructured":"Lohmann, C., Kuzmin, D., Shadid, J.N., Mabuza, S.: Flux-corrected transport algorithms for continuous Galerkin methods based on high order Bernstein finite elements. J. Comput. Phys. 344, 151\u2013186 (2017)","journal-title":"J. Comput. Phys."},{"key":"1922_CR33","doi-asserted-by":"publisher","first-page":"109345","DOI":"10.1016\/j.jcp.2020.109345","volume":"409","author":"J Magiera","year":"2020","unstructured":"Magiera, J., Ray, D., Hesthaven, J.S., Rohde, C.: Constraint-aware neural networks for riemann problems. J. Comput. Phys. 409, 109345 (2020)","journal-title":"J. Comput. Phys."},{"issue":"3\u20134","key":"1922_CR34","doi-asserted-by":"publisher","first-page":"311","DOI":"10.1007\/s10596-013-9387-6","volume":"18","author":"K Nikitin","year":"2014","unstructured":"Nikitin, K., Terekhov, K., Vassilevski, Y.: A monotone nonlinear finite volume method for diffusion equations and multiphase flows. Comput. Geosci. 18(3\u20134), 311\u2013324 (2014)","journal-title":"Comput. Geosci."},{"issue":"5","key":"1922_CR35","doi-asserted-by":"publisher","first-page":"955","DOI":"10.1137\/0721060","volume":"21","author":"S Osher","year":"1984","unstructured":"Osher, S., Chakravarthy, S.: High resolution schemes and the entropy condition. SIAM J. Numer. Anal. 21(5), 955\u2013984 (1984)","journal-title":"SIAM J. Numer. Anal."},{"issue":"1","key":"1922_CR36","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1006\/jcph.2002.7191","volume":"183","author":"J Qiu","year":"2002","unstructured":"Qiu, J., Shu, C.-W.: On the construction, comparison, and local characteristic decomposition for high-order central WENO schemes. J. Comput. Phys. 183(1), 187\u2013209 (2002)","journal-title":"J. Comput. Phys."},{"issue":"2","key":"1922_CR37","first-page":"267","volume":"1","author":"VV Rusanov","year":"1961","unstructured":"Rusanov, V.V.: The calculation of the interaction of non-stationary shock waves with barriers. Zhurnal Vychislitel\u2019noi Matematiki i Matematicheskoi Fiziki 1(2), 267\u2013279 (1961)","journal-title":"Zhurnal Vychislitel\u2019noi Matematiki i Matematicheskoi Fiziki"},{"key":"1922_CR38","doi-asserted-by":"publisher","first-page":"271","DOI":"10.1007\/BF01389573","volume":"42","author":"MN Spijker","year":"1983","unstructured":"Spijker, M.N.: Contractivity in the numerical solution of initial value problems. Numer. Math. 42, 271\u2013290 (1983)","journal-title":"Numer. Math."},{"issue":"2","key":"1922_CR39","doi-asserted-by":"publisher","first-page":"A583","DOI":"10.1137\/140965326","volume":"37","author":"T Xiong","year":"2015","unstructured":"Xiong, T., Qiu, J.-M., Zhengfu, X.: High order maximum-principle-preserving discontinuous Galerkin method for convection-diffusion equations. SIAM J. Sci. Comput. 37(2), A583\u2013A608 (2015)","journal-title":"SIAM J. Sci. Comput."},{"issue":"2","key":"1922_CR40","doi-asserted-by":"publisher","first-page":"795","DOI":"10.1007\/s10915-015-0104-6","volume":"67","author":"P Yang","year":"2016","unstructured":"Yang, P., Xiong, T., Qiu, J.-M., Zhengfu, X.: High order maximum principle preserving finite volume method for convection dominated problems. J. Sci. Comput. 67(2), 795\u2013820 (2016)","journal-title":"J. Sci. Comput."},{"issue":"3","key":"1922_CR41","doi-asserted-by":"publisher","first-page":"335","DOI":"10.1016\/0021-9991(79)90051-2","volume":"31","author":"ST Zalesak","year":"1979","unstructured":"Zalesak, S.T.: Fully multidimensional flux-corrected transport algorithms for fluids. J. Comput. Phys. 31(3), 335\u2013362 (1979)","journal-title":"J. Comput. Phys."},{"issue":"2","key":"1922_CR42","doi-asserted-by":"publisher","first-page":"A627","DOI":"10.1137\/110839230","volume":"34","author":"X Zhang","year":"2012","unstructured":"Zhang, X., Liu, Y., Shu, C.-W.: Maximum-principle-satisfying high order finite volume weighted essentially nonoscillatory schemes for convection-diffusion equations. SIAM J. Sci. Comput. 34(2), A627\u2013A658 (2012)","journal-title":"SIAM J. Sci. Comput."},{"issue":"9","key":"1922_CR43","doi-asserted-by":"publisher","first-page":"3091","DOI":"10.1016\/j.jcp.2009.12.030","volume":"229","author":"X Zhang","year":"2010","unstructured":"Zhang, X., Shu, C.-W.: On maximum-principle-satisfying high order schemes for scalar conservation laws. J. Comput. Phys. 229(9), 3091\u20133120 (2010)","journal-title":"J. Comput. Phys."},{"issue":"2134","key":"1922_CR44","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. Royal Soc. A: Math. Phys. Eng. Sci. 467(2134), 2752\u20132776 (2011)","journal-title":"Proc. Royal Soc. A: Math. Phys. Eng. Sci."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-022-01922-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10915-022-01922-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-022-01922-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,10,3]],"date-time":"2022-10-03T18:58:31Z","timestamp":1664823511000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10915-022-01922-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,8,1]]},"references-count":44,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2022,9]]}},"alternative-id":["1922"],"URL":"https:\/\/doi.org\/10.1007\/s10915-022-01922-8","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,8,1]]},"assertion":[{"value":"16 September 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 September 2021","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 June 2022","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 August 2022","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no known conflicts of interest, competing interests or personal relationships that could have appeared to influence the work reported in this paper.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"102"}}