{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,18]],"date-time":"2026-06-18T04:53:49Z","timestamp":1781758429094,"version":"3.54.5"},"reference-count":51,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Journal of Computational Physics"],"published-print":{"date-parts":[[2026,10]]},"DOI":"10.1016\/j.jcp.2026.115113","type":"journal-article","created":{"date-parts":[[2026,6,5]],"date-time":"2026-06-05T16:11:19Z","timestamp":1780675879000},"page":"115113","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["A subcell entropy-constrained limiter for entropy stable discontinuous Galerkin methods"],"prefix":"10.1016","volume":"563","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-9724-269X","authenticated-orcid":false,"given":"Zhihui","family":"Zhao","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ming","family":"Zhao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shixi","family":"Hao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qiushi","family":"Ding","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jiahuan","family":"Chen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhengxian","family":"Liu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"10.1016\/j.jcp.2026.115113_bib0001","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1023\/A:1012873910884","article-title":"Runge-Kutta discontinuous Galerkin methods for convection-dominated problems","volume":"16","author":"Cockburn","year":"2001","journal-title":"J. Sci. Comput."},{"key":"10.1016\/j.jcp.2026.115113_bib0002","doi-asserted-by":"crossref","first-page":"2440","DOI":"10.1137\/S0036142997316712","article-title":"The local discontinuous Galerkin method for time-dependent convection-diffusion systems","volume":"35","author":"Cockburn","year":"1998","journal-title":"SIAM J. Numer. Anal."},{"key":"10.1016\/j.jcp.2026.115113_bib0003","series-title":"Proceedings of the 18th AIAA Computational Fluid Dynamics Conference","article-title":"A flux reconstruction approach to high-order schemes including discontinuous Galerkin methods","author":"Huynh","year":"2007"},{"key":"10.1016\/j.jcp.2026.115113_bib0004","doi-asserted-by":"crossref","DOI":"10.1016\/j.compfluid.2021.105175","article-title":"A hierarchical reconstruction for DG\/FV method with low dispersion: basic formulation and applications","volume":"231","author":"Zhao","year":"2021","journal-title":"Comput. Fluids"},{"key":"10.1016\/j.jcp.2026.115113_bib0005","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1017\/S0962492902000156","article-title":"Entropy stability theory for difference approximations of nonlinear conservation laws and related time-dependent problems","volume":"12","author":"Tadmor","year":"2003","journal-title":"Acta Numer."},{"key":"10.1016\/j.jcp.2026.115113_bib0006","doi-asserted-by":"crossref","first-page":"518","DOI":"10.1016\/j.jcp.2013.06.014","article-title":"High-order entropy stable finite difference schemes for nonlinear conservation laws: finite domain","volume":"252","author":"Fisher","year":"2013","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.jcp.2026.115113_bib0007","series-title":"Spectral\/hp Element Methods for CFD","author":"Karniadakis","year":"1999"},{"key":"10.1016\/j.jcp.2026.115113_bib0008","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1016\/S0021-9991(03)00314-0","article-title":"De-aliasing on non-uniform grids: algorithms and applications","volume":"191","author":"Kirby","year":"2003","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.jcp.2026.115113_bib0009","unstructured":"B. Christner, J. Chan, (2025). Entropy stable nodal discontinuous Galerkin methods via quadratic knapsack limiting, arXiv:2507.14488."},{"key":"10.1016\/j.jcp.2026.115113_bib0010","doi-asserted-by":"crossref","first-page":"1262","DOI":"10.1007\/s10915-017-0585-6","article-title":"Insights on aliasing driven instabilities for advection equations with application to Gauss\u2013Lobatto discontinuous Galerkin methods","volume":"75","author":"Manzanero","year":"2018","journal-title":"J. Sci. Comput."},{"key":"10.1016\/j.jcp.2026.115113_bib0011","series-title":"Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications","author":"Hesthaven","year":"2008"},{"key":"10.1016\/j.jcp.2026.115113_bib0012","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1016\/j.compfluid.2012.03.006","article-title":"Explicit discontinuous Galerkin methods for unsteady problems","volume":"61","author":"Hindenlang","year":"2012","journal-title":"Comput. Fluids"},{"key":"10.1016\/j.jcp.2026.115113_bib0013","doi-asserted-by":"crossref","first-page":"A1233","DOI":"10.1137\/120890144","article-title":"A skew-symmetric discontinuous Galerkin spectral element discretization and its relation to SBP-SAT finite difference methods","volume":"35","author":"Gassner","year":"2013","journal-title":"SIAM J. Sci. Comput."},{"key":"10.1016\/j.jcp.2026.115113_bib0014","doi-asserted-by":"crossref","first-page":"B835","DOI":"10.1137\/130932193","article-title":"Entropy stable spectral collocation schemes for the Navier-Stokes equations: discontinuous interfaces","volume":"36","author":"Carpenter","year":"2014","journal-title":"SIAM J. Sci. Comput."},{"key":"10.1016\/j.jcp.2026.115113_bib0015","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/j.jcp.2016.09.013","article-title":"Split form nodal discontinuous Galerkin schemes with summation-by-parts property for the compressible Euler equations","volume":"327","author":"Gassner","year":"2016","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.jcp.2026.115113_bib0016","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1007\/s10915-022-01935-3","article-title":"A unifying algebraic framework for discontinuous Galerkin and flux reconstruction methods based on the summation-by-parts property","volume":"92","author":"Montoya","year":"2022","journal-title":"J. Sci. Comput."},{"key":"10.1016\/j.jcp.2026.115113_bib0017","doi-asserted-by":"crossref","first-page":"1","DOI":"10.4208\/csiam-am.2020-0003","article-title":"Review of entropy stable discontinuous Galerkin methods for systems of conservation laws on unstructured simplex meshes","volume":"1","author":"Chen","year":"2020","journal-title":"CSIAM Trans. Appl. Math."},{"key":"10.1016\/j.jcp.2026.115113_bib0018","doi-asserted-by":"crossref","DOI":"10.1016\/j.jcp.2021.110475","article-title":"A data-driven high order sub-cell artificial viscosity for the discontinuous Galerkin spectral element method","volume":"441","author":"Zeifang","year":"2021","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.jcp.2026.115113_bib0019","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1016\/j.cma.2012.08.018","article-title":"Implementation of the entropy viscosity method with the discontinuous Galerkin method","volume":"253","author":"Zingan","year":"2013","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"10.1016\/j.jcp.2026.115113_bib0020","doi-asserted-by":"crossref","first-page":"2566","DOI":"10.1002\/nme.1172","article-title":"New two-dimensional slope limiters for discontinuous Galerkin methods on arbitrary meshes","volume":"61","author":"Hoteit","year":"2004","journal-title":"Int. J. Numer. Meth. Eng."},{"key":"10.1016\/j.jcp.2026.115113_bib0021","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1006\/jcph.2001.6718","article-title":"A problem-independent limiter for high-order Runge-Kutta discontinuous Galerkin methods","volume":"169","author":"Burbeau","year":"2001","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.jcp.2026.115113_bib0022","doi-asserted-by":"crossref","DOI":"10.1016\/j.jcp.2021.110188","article-title":"A high-order moment limiter for the discontinuous Galerkin method on triangular meshes","volume":"433","author":"Dutt","year":"2021","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.jcp.2026.115113_bib0023","doi-asserted-by":"crossref","first-page":"451","DOI":"10.4208\/aamm.09-m0913","article-title":"A parameter-free generalized moment limiter for high-order methods on unstructured grids","volume":"4","author":"Yang","year":"2009","journal-title":"Adv. Appl. Math. Mech."},{"key":"10.1016\/j.jcp.2026.115113_bib0024","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1016\/j.jcp.2018.10.050","article-title":"A posteriori correction of high-order discontinuous Galerkin scheme through subcell finite volume formulation and flux reconstruction","volume":"387","author":"Vilar","year":"2019","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.jcp.2026.115113_bib0025","doi-asserted-by":"crossref","first-page":"2566","DOI":"10.1002\/nme.1172","article-title":"New two-dimensional slope limiters for discontinuous Galerkin methods on arbitrary meshes","volume":"61","author":"Hoteit","year":"2004","journal-title":"Int. J. Numer. Methods Eng."},{"key":"10.1016\/j.jcp.2026.115113_bib0026","doi-asserted-by":"crossref","DOI":"10.1016\/j.compfluid.2026.107045","article-title":"A hierarchical multi-resolution WENO limiter for Runge-Kutta discontinuous Galerkin methods","volume":"312","author":"Ding","year":"2026","journal-title":"Comput. Fluids"},{"key":"10.1016\/j.jcp.2026.115113_bib0027","doi-asserted-by":"crossref","first-page":"598","DOI":"10.1016\/j.jcp.2016.04.030","article-title":"High order WENO and DG methods for time-dependent convection-dominated PDEs: a brief survey of several recent developments","volume":"316","author":"Shu","year":"2016","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.jcp.2026.115113_bib0028","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1016\/j.jcp.2012.08.028","article-title":"A simple weighted essentially nonoscillatory limiter for Runge-Kutta discontinuous Galerkin methods","volume":"232","author":"Zhong","year":"2013","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.jcp.2026.115113_bib0029","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1016\/j.jcp.2017.05.025","article-title":"Entropy stable high order discontinuous Galerkin methods with suitable quadrature rules for hyperbolic conservation laws","volume":"345","author":"Chen","year":"2017","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.jcp.2026.115113_bib0030","doi-asserted-by":"crossref","first-page":"A1132","DOI":"10.1137\/22M1524151","article-title":"An entropy stable essentially oscillation-free discontinuous Galerkin method for hyperbolic conservation laws","volume":"46","author":"Liu","year":"2024","journal-title":"SIAM J. Sci. Comput."},{"key":"10.1016\/j.jcp.2026.115113_bib0031","doi-asserted-by":"crossref","DOI":"10.1016\/j.jcp.2025.114380","article-title":"An artificial viscosity approach to high order entropy stable discontinuous Galerkin methods","volume":"543","author":"Chan","year":"2025","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.jcp.2026.115113_bib0032","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1016\/j.jcp.2014.08.009","article-title":"A posteriori subcell limiting of the discontinuous Galerkin finite element method for hyperbolic conservation laws","volume":"278","author":"Dumbser","year":"2014","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.jcp.2026.115113_bib0033","doi-asserted-by":"crossref","DOI":"10.1016\/j.cma.2021.113876","article-title":"Sparse invariant domain preserving discontinuous Galerkin methods with subcell convex limiting","volume":"382","author":"Pazner","year":"2021","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"10.1016\/j.jcp.2026.115113_bib0034","doi-asserted-by":"crossref","DOI":"10.1016\/j.jcp.2020.109935","article-title":"A provably entropy stable subcell shock capturing approach for high order split form DG for the compressible Euler equations","volume":"426","author":"Hennemann","year":"2021","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.jcp.2026.115113_bib0035","doi-asserted-by":"crossref","DOI":"10.1016\/j.compfluid.2022.105627","article-title":"Subcell limiting strategies for discontinuous Galerkin spectral element methods","volume":"247","author":"Rueda-Ram\u00edrez","year":"2022","journal-title":"Comput. Fluids."},{"key":"10.1016\/j.jcp.2026.115113_bib0036","doi-asserted-by":"crossref","DOI":"10.1016\/j.cma.2021.114428","article-title":"Limiter-based entropy stabilization of semi-discrete and fully discrete schemes for nonlinear hyperbolic problems","volume":"389","author":"Kuzmin","year":"2022","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"10.1016\/j.jcp.2026.115113_bib0037","doi-asserted-by":"crossref","first-page":"1860","DOI":"10.1007\/s42967-023-00321-6","article-title":"Monolithic Convex limiting for Legendre-Gauss-Lobatto discontinuous galerkin spectral-element methods","volume":"6","author":"Rueda-Ram\u00edrez","year":"2024","journal-title":"Commun. Appl. Math. Comput."},{"key":"10.1016\/j.jcp.2026.115113_bib0038","doi-asserted-by":"crossref","DOI":"10.1016\/j.jcp.2023.112677","article-title":"High order entropy stable discontinuous Galerkin spectral element methods through subcell limiting","volume":"498","author":"Lin","year":"2024","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.jcp.2026.115113_bib0039","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1090\/S0025-5718-1987-0890255-3","article-title":"The numerical viscosity of entropy stable schemes for systems of conservation laws. I","volume":"49","author":"Tadmor","year":"1987","journal-title":"Math. Comp."},{"key":"10.1016\/j.jcp.2026.115113_bib0040","doi-asserted-by":"crossref","first-page":"216","DOI":"10.1007\/s10915-017-0618-1","article-title":"Comparison of some entropy conservative numerical fluxes for the euler equations","volume":"76","author":"Ranocha","year":"2018","journal-title":"J. Sci. Comput."},{"key":"10.1016\/j.jcp.2026.115113_bib0041","first-page":"1","article-title":"Sub-cell shock capturing for discontinuous Galerkin methods","author":"Persson","year":"2006"},{"key":"10.1016\/j.jcp.2026.115113_bib0042","series-title":"Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018, Lecture Notes in Computational Science and Engineering","first-page":"525","article-title":"Entropy conserving and kinetic energy preserving numerical methods for the Euler equations using summation-by-parts operators","volume":"134","author":"Ranocha","year":"2020"},{"key":"10.1016\/j.jcp.2026.115113_bib0043","article-title":"Fourth-order 2N-storage Runge-Kutta schemes","author":"Carpenter","year":"1994","journal-title":"Tech. Rep. NASA TM"},{"key":"10.1016\/j.jcp.2026.115113_bib0044","doi-asserted-by":"crossref","first-page":"202","DOI":"10.1006\/jcph.1996.0130","article-title":"Efficient implementation of weighted ENO schemes","volume":"126","author":"Jiang","year":"1996","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.jcp.2026.115113_bib0045","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0021-9991(78)90023-2","article-title":"A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws","volume":"27","author":"Sod","year":"1978","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.jcp.2026.115113_bib0046","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1016\/0021-9991(88)90177-5","article-title":"Efficient implementation of essentially non-oscillatory shock-capturing schemes","volume":"77","author":"Shu","year":"1988","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.jcp.2026.115113_bib0047","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1016\/0021-9991(84)90142-6","article-title":"The numerical simulation of two-dimensional fluid flow with strong shocks","volume":"54","author":"Woodward","year":"1984","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.jcp.2026.115113_bib0048","doi-asserted-by":"crossref","first-page":"384","DOI":"10.1134\/S0015462814030107","article-title":"Wave generation on an interface by vortex disturbances in a shear flow","volume":"49","author":"Kalashnik","year":"2014","journal-title":"Fluid Dyn."},{"key":"10.1016\/j.jcp.2026.115113_bib0049","doi-asserted-by":"crossref","unstructured":"H. Ranocha, M. Schlottke-Lakemper, A.R. Winters, E. Faulhaber, J. Chan, G. Gassner, Adaptive numerical simulations with Trixi.jl: A case study of Julia for scientific computing, in: Proceedings of the JuliaCon Conferences 1(1), 2022, p. 77, arXiv:2108.06476.","DOI":"10.21105\/jcon.00077"},{"key":"10.1016\/j.jcp.2026.115113_bib0050","doi-asserted-by":"crossref","first-page":"2381","DOI":"10.1137\/040614189","article-title":"Adaptive semidiscrete central-upwind schemes for nonconvex hyperbolic conservation laws","volume":"29","author":"Kurganov","year":"2007","journal-title":"SIAM J. Sci. Comput."},{"key":"10.1016\/j.jcp.2026.115113_bib0051","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1016\/j.jcp.2015.06.032","article-title":"Dealiasing techniques for high-order spectral element methods on regular and irregular grids","volume":"299","author":"Mengaldo","year":"2015","journal-title":"J. Comput. Phys."}],"container-title":["Journal of Computational Physics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0021999126004651?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0021999126004651?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,6,18]],"date-time":"2026-06-18T04:19:15Z","timestamp":1781756355000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0021999126004651"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,10]]},"references-count":51,"alternative-id":["S0021999126004651"],"URL":"https:\/\/doi.org\/10.1016\/j.jcp.2026.115113","relation":{},"ISSN":["0021-9991"],"issn-type":[{"value":"0021-9991","type":"print"}],"subject":[],"published":{"date-parts":[[2026,10]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"A subcell entropy-constrained limiter for entropy stable discontinuous Galerkin methods","name":"articletitle","label":"Article Title"},{"value":"Journal of Computational Physics","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.jcp.2026.115113","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"115113"}}