Ricardo, Kieran; Lee, Dave; Duru, Kenneth Conservation and stability in a discontinuous Galerkin method for the vector invariant spherical shallow water equations. (English) Zbl 07811344 J. Comput. Phys. 500, Article ID 112763, 15 p. (2024). MSC: 65Mxx 76Mxx 86Axx PDFBibTeX XMLCite \textit{K. Ricardo} et al., J. Comput. Phys. 500, Article ID 112763, 15 p. (2024; Zbl 07811344) Full Text: DOI arXiv
Ricardo, Kieran; Lee, David; Duru, Kenneth Entropy and energy conservation for thermal atmospheric dynamics using mixed compatible finite elements. (English) Zbl 07808004 J. Comput. Phys. 496, Article ID 112605, 15 p. (2024). MSC: 65Mxx 86Axx 65Nxx PDFBibTeX XMLCite \textit{K. Ricardo} et al., J. Comput. Phys. 496, Article ID 112605, 15 p. (2024; Zbl 07808004) Full Text: DOI arXiv
Ersing, Patrick; Winters, Andrew R. An entropy stable discontinuous Galerkin method for the two-layer shallow water equations on curvilinear meshes. (English) Zbl 07807895 J. Sci. Comput. 98, No. 3, Paper No. 62, 35 p. (2024). Reviewer: Denys Dutykh (Le Bourget-du-Lac) MSC: 65M70 65M60 65M06 65L06 65N35 65N30 65D32 65M12 76B15 76T06 86A05 76M22 35L50 35Q30 PDFBibTeX XMLCite \textit{P. Ersing} and \textit{A. R. Winters}, J. Sci. Comput. 98, No. 3, Paper No. 62, 35 p. (2024; Zbl 07807895) Full Text: DOI arXiv OA License
Xu, Linfeng; Ding, Shengrong; Wu, Kailiang High-order accurate entropy stable schemes for relativistic hydrodynamics with general Synge-type equation of state. (English) Zbl 07794698 J. Sci. Comput. 98, No. 2, Paper No. 43, 62 p. (2024). MSC: 65L10 PDFBibTeX XMLCite \textit{L. Xu} et al., J. Sci. Comput. 98, No. 2, Paper No. 43, 62 p. (2024; Zbl 07794698) Full Text: DOI
Guo, Wei; Chen, Ziming; Qian, Shouguo; Li, Gang; Niu, Qiang A new well-balanced finite volume CWENO scheme for shallow water equations over bottom topography. (English) Zbl 07787032 Adv. Appl. Math. Mech. 15, No. 6, 1515-1539 (2023). MSC: 74S10 PDFBibTeX XMLCite \textit{W. Guo} et al., Adv. Appl. Math. Mech. 15, No. 6, 1515--1539 (2023; Zbl 07787032) Full Text: DOI
Bhoriya, Deepak; Biswas, Biswarup; Kumar, Harish; Chandrashekhar, Praveen Entropy stable discontinuous Galerkin schemes for two-fluid relativistic plasma flow equations. (English) Zbl 07766142 J. Sci. Comput. 97, No. 3, Paper No. 72, 40 p. (2023). MSC: 65-XX 35L25 35L56 35L75 65M60 PDFBibTeX XMLCite \textit{D. Bhoriya} et al., J. Sci. Comput. 97, No. 3, Paper No. 72, 40 p. (2023; Zbl 07766142) Full Text: DOI arXiv
Ziggaf, Moussa; Kissami, Imad; Boubekeur, Mohamed; Benkhaldoun, Fayssal A well-balanced FVC scheme for 2D shallow water flows on unstructured triangular meshes. (English) Zbl 1524.65464 Adv. Appl. Math. Mech. 15, No. 5, 1335-1378 (2023). MSC: 65M08 35L65 76M12 65M25 76B15 76U05 35R35 65M06 65N08 76M20 PDFBibTeX XMLCite \textit{M. Ziggaf} et al., Adv. Appl. Math. Mech. 15, No. 5, 1335--1378 (2023; Zbl 1524.65464) Full Text: DOI arXiv
Kerkhoff, Xenia; May, Sandra Commutative properties for conservative space-time DG discretizations of optimal control problems involving the viscous Burgers equation. (English) Zbl 1516.49030 Math. Control Relat. Fields 13, No. 1, 193-214 (2023). MSC: 49M41 65M60 PDFBibTeX XMLCite \textit{X. Kerkhoff} and \textit{S. May}, Math. Control Relat. Fields 13, No. 1, 193--214 (2023; Zbl 1516.49030) Full Text: DOI
Abgrall, R.; Nordström, J.; Öffner, P.; Tokareva, S. Analysis of the SBP-SAT stabilization for finite element methods. II: Entropy stability. (English) Zbl 1524.65498 Commun. Appl. Math. Comput. 5, No. 2, 573-595 (2023). MSC: 65M60 65M12 65M06 65N30 65M15 PDFBibTeX XMLCite \textit{R. Abgrall} et al., Commun. Appl. Math. Comput. 5, No. 2, 573--595 (2023; Zbl 1524.65498) Full Text: DOI arXiv
Busto, Saray; Dumbser, Michael A new thermodynamically compatible finite volume scheme for magnetohydrodynamics. (English) Zbl 07670867 SIAM J. Numer. Anal. 61, No. 1, 343-364 (2023). MSC: 65-XX 35L40 65M08 PDFBibTeX XMLCite \textit{S. Busto} and \textit{M. Dumbser}, SIAM J. Numer. Anal. 61, No. 1, 343--364 (2023; Zbl 07670867) Full Text: DOI arXiv
Kriksin, Yu. A.; Tishkin, V. F. Entropic regularization of the discontinuous Galerkin method for two-dimensional Euler equations in triangulated domains. (Russian. English summary) Zbl 07665524 Mat. Model. 35, No. 3, 3-19 (2023). MSC: 65-XX 76-XX PDFBibTeX XMLCite \textit{Yu. A. Kriksin} and \textit{V. F. Tishkin}, Mat. Model. 35, No. 3, 3--19 (2023; Zbl 07665524) Full Text: DOI MNR
Yan, Ge; Kaur, Sharanjeet; Banks, Jeffrey W.; Hicken, Jason E. Entropy-stable discontinuous Galerkin difference methods for hyperbolic conservation laws. (English) Zbl 1499.65542 J. Comput. Appl. Math. 422, Article ID 114885, 24 p. (2023). MSC: 65M60 65M06 35L65 65M12 PDFBibTeX XMLCite \textit{G. Yan} et al., J. Comput. Appl. Math. 422, Article ID 114885, 24 p. (2023; Zbl 1499.65542) Full Text: DOI arXiv
Gaburro, Elena; Öffner, Philipp; Ricchiuto, Mario; Torlo, Davide High order entropy preserving ADER-DG schemes. (English) Zbl 1511.65109 Appl. Math. Comput. 440, Article ID 127644, 21 p. (2023). MSC: 65M70 65L06 35L65 65L20 65M12 65P10 PDFBibTeX XMLCite \textit{E. Gaburro} et al., Appl. Math. Comput. 440, Article ID 127644, 21 p. (2023; Zbl 1511.65109) Full Text: DOI arXiv
Abgrall, Rémi; Busto, Saray; Dumbser, Michael A simple and general framework for the construction of thermodynamically compatible schemes for computational fluid and solid mechanics. (English) Zbl 1510.76098 Appl. Math. Comput. 440, Article ID 127629, 40 p. (2023). MSC: 76M12 76M10 65M08 65M12 65M60 76B15 PDFBibTeX XMLCite \textit{R. Abgrall} et al., Appl. Math. Comput. 440, Article ID 127629, 40 p. (2023; Zbl 1510.76098) Full Text: DOI
Busto, Saray; Dumbser, Michael A new family of thermodynamically compatible discontinuous Galerkin methods for continuum mechanics and turbulent shallow water flows. (English) Zbl 1503.65223 J. Sci. Comput. 93, No. 2, Paper No. 56, 40 p. (2022). MSC: 65M60 65L06 65N30 65M12 76F10 76B15 76D05 76N06 76M10 74B20 74S05 80A19 35L02 35Q31 35Q30 35Q79 PDFBibTeX XMLCite \textit{S. Busto} and \textit{M. Dumbser}, J. Sci. Comput. 93, No. 2, Paper No. 56, 40 p. (2022; Zbl 1503.65223) Full Text: DOI
Kopriva, David A.; Gassner, Gregor J.; Nordström, Jan On the theoretical foundation of overset grid methods for hyperbolic problems. II: Entropy bounded formulations for nonlinear conservation laws. (English) Zbl 07605591 J. Comput. Phys. 471, Article ID 111620, 18 p. (2022). MSC: 65Mxx 76Mxx 76Nxx PDFBibTeX XMLCite \textit{D. A. Kopriva} et al., J. Comput. Phys. 471, Article ID 111620, 18 p. (2022; Zbl 07605591) Full Text: DOI arXiv
Fu, Guosheng A high-order velocity-based discontinuous Galerkin scheme for the shallow water equations: local conservation, entropy stability, well-balanced property, and positivity preservation. (English) Zbl 1495.65211 J. Sci. Comput. 92, No. 3, Paper No. 86, 33 p. (2022). MSC: 65N30 65N12 76S05 76D07 PDFBibTeX XMLCite \textit{G. Fu}, J. Sci. Comput. 92, No. 3, Paper No. 86, 33 p. (2022; Zbl 1495.65211) Full Text: DOI arXiv
Busto, Saray; Dumbser, Michael; Peshkov, Ilya; Romenski, Evgeniy On thermodynamically compatible finite volume schemes for continuum mechanics. (English) Zbl 07556268 SIAM J. Sci. Comput. 44, No. 3, A1723-A1751 (2022). MSC: 65-XX 35L40 65M08 PDFBibTeX XMLCite \textit{S. Busto} et al., SIAM J. Sci. Comput. 44, No. 3, A1723--A1751 (2022; Zbl 07556268) Full Text: DOI
Nordström, Jan; Winters, Andrew R. A linear and nonlinear analysis of the shallow water equations and its impact on boundary conditions. (English) Zbl 07536758 J. Comput. Phys. 463, Article ID 111254, 15 p. (2022). MSC: 65Mxx 35Lxx 76Mxx PDFBibTeX XMLCite \textit{J. Nordström} and \textit{A. R. Winters}, J. Comput. Phys. 463, Article ID 111254, 15 p. (2022; Zbl 07536758) Full Text: DOI arXiv
Izem, Nouh; Seaid, Mohammed A well-balanced Runge-Kutta discontinuous Galerkin method for multilayer shallow water equations with non-flat bottom topography. (English) Zbl 1499.65496 Adv. Appl. Math. Mech. 14, No. 3, 725-758 (2022). MSC: 65M60 35L65 76B15 86A05 PDFBibTeX XMLCite \textit{N. Izem} and \textit{M. Seaid}, Adv. Appl. Math. Mech. 14, No. 3, 725--758 (2022; Zbl 1499.65496) Full Text: DOI
Valseth, Eirik; Dawson, Clint A stable space-time FE method for the shallow water equations. (English) Zbl 1484.76045 Comput. Geosci. 26, No. 1, 53-70 (2022). MSC: 76M10 65M60 PDFBibTeX XMLCite \textit{E. Valseth} and \textit{C. Dawson}, Comput. Geosci. 26, No. 1, 53--70 (2022; Zbl 1484.76045) Full Text: DOI arXiv
Biswas, Biswarup; Kumar, Harish; Bhoriya, Deepak Entropy stable discontinuous Galerkin schemes for the special relativistic hydrodynamics equations. (English) Zbl 1524.35379 Comput. Math. Appl. 112, 55-75 (2022). MSC: 35L65 76Y05 65M60 65M06 65M12 PDFBibTeX XMLCite \textit{B. Biswas} et al., Comput. Math. Appl. 112, 55--75 (2022; Zbl 1524.35379) Full Text: DOI
Busto, S.; Dumbser, M. A staggered semi-implicit hybrid finite volume / finite element scheme for the shallow water equations at all Froude numbers. (English) Zbl 1485.76056 Appl. Numer. Math. 175, 108-132 (2022). MSC: 76M12 76M10 76B10 PDFBibTeX XMLCite \textit{S. Busto} and \textit{M. Dumbser}, Appl. Numer. Math. 175, 108--132 (2022; Zbl 1485.76056) Full Text: DOI
Colombo, A.; Crivellini, A.; Nigro, A. On the entropy conserving/stable implicit DG discretization of the Euler equations in entropy variables. (English) Zbl 1521.76323 Comput. Fluids 232, Article ID 105198, 21 p. (2022). MSC: 76M10 76Nxx PDFBibTeX XMLCite \textit{A. Colombo} et al., Comput. Fluids 232, Article ID 105198, 21 p. (2022; Zbl 1521.76323) Full Text: DOI
Qiao, Dianliang; Lin, Zhiyang; Guo, Mingmin; Yang, Xiaoxia; Li, Xiaoyang; Zhang, Peng; Zhang, Xiaoning Riemann solvers of a conserved high-order traffic flow model with discontinuous fluxes. (English) Zbl 1510.65205 Appl. Math. Comput. 413, Article ID 126648, 11 p. (2022). MSC: 65M06 35L65 PDFBibTeX XMLCite \textit{D. Qiao} et al., Appl. Math. Comput. 413, Article ID 126648, 11 p. (2022; Zbl 1510.65205) Full Text: DOI
Biswas, Biswarup; Kumar, Harish; Yadav, Anshu Entropy stable discontinuous Galerkin methods for ten-moment Gaussian closure equations. (English) Zbl 07511459 J. Comput. Phys. 431, Article ID 110148, 23 p. (2021). MSC: 65Mxx 35Lxx 76Mxx PDFBibTeX XMLCite \textit{B. Biswas} et al., J. Comput. Phys. 431, Article ID 110148, 23 p. (2021; Zbl 07511459) Full Text: DOI arXiv
Duan, Junming; Tang, Huazhong High-order accurate entropy stable finite difference schemes for the shallow water magnetohydrodynamics. (English) Zbl 07511453 J. Comput. Phys. 431, Article ID 110136, 26 p. (2021). MSC: 65Mxx 76Mxx 35Lxx PDFBibTeX XMLCite \textit{J. Duan} and \textit{H. Tang}, J. Comput. Phys. 431, Article ID 110136, 26 p. (2021; Zbl 07511453) Full Text: DOI arXiv
Rojas, Diego; Boukharfane, Radouan; Dalcin, Lisandro; Del Rey Fernández, David C.; Ranocha, Hendrik; Keyes, David E.; Parsani, Matteo On the robustness and performance of entropy stable collocated discontinuous Galerkin methods. (English) Zbl 07510039 J. Comput. Phys. 426, Article ID 109891, 17 p. (2021). MSC: 76-XX 65-XX PDFBibTeX XMLCite \textit{D. Rojas} et al., J. Comput. Phys. 426, Article ID 109891, 17 p. (2021; Zbl 07510039) Full Text: DOI arXiv
Bragin, M. D.; Kriksin, Yu. A.; Tishkin, V. F. Entropic regularization of the discontinuous Galerkin method in conservative variables for two-dimensional Euler equations. (Russian. English summary) Zbl 1484.76038 Mat. Model. 33, No. 12, 49-66 (2021). MSC: 76M10 76M20 76N15 PDFBibTeX XMLCite \textit{M. D. Bragin} et al., Mat. Model. 33, No. 12, 49--66 (2021; Zbl 1484.76038) Full Text: DOI MNR
Ranocha, Hendrik; de Luna, Manuel Quezada; Ketcheson, David I. On the rate of error growth in time for numerical solutions of nonlinear dispersive wave equations. (English) Zbl 1476.65271 SN Partial Differ. Equ. Appl. 2, No. 6, Paper No. 76, 26 p. (2021). MSC: 65M70 65M15 35Q35 PDFBibTeX XMLCite \textit{H. Ranocha} et al., SN Partial Differ. Equ. Appl. 2, No. 6, Paper No. 76, 26 p. (2021; Zbl 1476.65271) Full Text: DOI arXiv
Yildiz, Süleyman; Uzunca, Murat; Karasözen, Bülent Structure-preserving reduced-order modeling of non-traditional shallow water equation. (English) Zbl 1480.93068 Benner, Peter (ed.) et al., Model reduction of complex dynamical systems. Selected papers based on the presentations at the workshop, University of Graz, Graz, Austria, August 28–30, 2019. Cham: Birkhäuser. ISNM, Int. Ser. Numer. Math. 171, 327-345 (2021). MSC: 93B11 93C20 93C15 65M06 PDFBibTeX XMLCite \textit{S. Yildiz} et al., ISNM, Int. Ser. Numer. Math. 171, 327--345 (2021; Zbl 1480.93068) Full Text: DOI arXiv
Li, Jiaojiao; Li, Gang; Qian, Shouguo; Gao, Jinmei High-order well-balanced finite volume WENO schemes with conservative variables decomposition for shallow water equations. (English) Zbl 1488.74132 Adv. Appl. Math. Mech. 13, No. 4, 827-849 (2021). MSC: 74S05 76B10 PDFBibTeX XMLCite \textit{J. Li} et al., Adv. Appl. Math. Mech. 13, No. 4, 827--849 (2021; Zbl 1488.74132) Full Text: DOI
Winters, Andrew R.; Kopriva, David A.; Gassner, Gregor J.; Hindenlang, Florian Construction of modern robust nodal discontinuous Galerkin spectral element methods for the compressible Navier-Stokes equations. (English) Zbl 1472.76066 Kronbichler, Martin (ed.) et al., Efficient high-order discretizations for computational fluid dynamics. Selected papers based on the presentations at the summer school, Udine, Italy, July 16–20, 2018. Cham: Springer. CISM Courses Lect. 602, 117-196 (2021). MSC: 76M22 76N06 PDFBibTeX XMLCite \textit{A. R. Winters} et al., CISM Courses Lect. 602, 117--196 (2021; Zbl 1472.76066) Full Text: DOI arXiv
Busto, Saray; Dumbser, Michael; Gavrilyuk, Sergey; Ivanova, Kseniya On thermodynamically compatible finite volume methods and path-conservative ADER discontinuous Galerkin schemes for turbulent shallow water flows. (English) Zbl 1501.65047 J. Sci. Comput. 88, No. 1, Paper No. 28, 45 p. (2021). Reviewer: Abdallah Bradji (Annaba) MSC: 65M08 65M06 65N08 65M60 35L02 35L45 76B15 76F50 76N10 76M10 76M12 35Q31 PDFBibTeX XMLCite \textit{S. Busto} et al., J. Sci. Comput. 88, No. 1, Paper No. 28, 45 p. (2021; Zbl 1501.65047) Full Text: DOI
Wu, Xinhui; Chan, Jesse Entropy stable discontinuous Galerkin methods for nonlinear conservation laws on networks and multi-dimensional domains. (English) Zbl 1467.62187 J. Sci. Comput. 87, No. 3, Paper No. 100, 34 p. (2021). MSC: 65M60 65M12 35L65 76M10 PDFBibTeX XMLCite \textit{X. Wu} and \textit{J. Chan}, J. Sci. Comput. 87, No. 3, Paper No. 100, 34 p. (2021; Zbl 1467.62187) Full Text: DOI arXiv
Li, Gang; Li, Jiaojiao; Qian, Shouguo; Gao, Jinmei A well-balanced ADER discontinuous Galerkin method based on differential transformation procedure for shallow water equations. (English) Zbl 1465.76063 Appl. Math. Comput. 395, Article ID 125848, 20 p. (2021). MSC: 76M12 76B99 PDFBibTeX XMLCite \textit{G. Li} et al., Appl. Math. Comput. 395, Article ID 125848, 20 p. (2021; Zbl 1465.76063) Full Text: DOI
Bragin, M. D.; Kriksin, Y. A.; Tishkin, V. F. Entropy stable discontinuous Galerkin method for two-dimensional Euler equations. (Russian. English summary) Zbl 1461.76344 Mat. Model. 33, No. 2, 125-140 (2021). Reviewer: Calin Ioan Gheorghiu (Cluj-Napoca) MSC: 76M10 76N15 65M60 PDFBibTeX XMLCite \textit{M. D. Bragin} et al., Mat. Model. 33, No. 2, 125--140 (2021; Zbl 1461.76344) Full Text: DOI MNR
Wu, Xinhui; Kubatko, Ethan J.; Chan, Jesse High-order entropy stable discontinuous Galerkin methods for the shallow water equations: curved triangular meshes and GPU acceleration. (English) Zbl 1524.65613 Comput. Math. Appl. 82, 179-199 (2021). MSC: 65M60 35L65 65M12 76B15 65M70 35Q35 65Y10 65N50 65M06 65N30 65N35 PDFBibTeX XMLCite \textit{X. Wu} et al., Comput. Math. Appl. 82, 179--199 (2021; Zbl 1524.65613) Full Text: DOI arXiv
Lundgren, Lukas; Mattsson, Ken An efficient finite difference method for the shallow water equations. (English) Zbl 07508393 J. Comput. Phys. 422, Article ID 109784, 28 p. (2020). MSC: 76-XX 65-XX PDFBibTeX XMLCite \textit{L. Lundgren} and \textit{K. Mattsson}, J. Comput. Phys. 422, Article ID 109784, 28 p. (2020; Zbl 07508393) Full Text: DOI
Duan, Junming; Tang, Huazhong High-order accurate entropy stable nodal discontinuous Galerkin schemes for the ideal special relativistic magnetohydrodynamics. (English) Zbl 07508357 J. Comput. Phys. 421, Article ID 109731, 32 p. (2020). MSC: 76-XX 65-XX PDFBibTeX XMLCite \textit{J. Duan} and \textit{H. Tang}, J. Comput. Phys. 421, Article ID 109731, 32 p. (2020; Zbl 07508357) Full Text: DOI arXiv
Manzanero, Juan; Rubio, Gonzalo; Kopriva, David A.; Ferrer, Esteban; Valero, Eusebio Entropy-stable discontinuous Galerkin approximation with summation-by-parts property for the incompressible Navier-Stokes/Cahn-Hilliard system. (English) Zbl 07505633 J. Comput. Phys. 408, Article ID 109363, 38 p. (2020). MSC: 76-XX 82-XX PDFBibTeX XMLCite \textit{J. Manzanero} et al., J. Comput. Phys. 408, Article ID 109363, 38 p. (2020; Zbl 07505633) Full Text: DOI arXiv
Ranocha, Hendrik Entropy conserving and kinetic energy preserving numerical methods for the Euler equations using summation-by-parts operators. (English) Zbl 1484.65233 Sherwin, Spencer J. (ed.) et al., Spectral and high order methods for partial differential equations, ICOSAHOM 2018. Selected papers from the ICOSAHOM conference, London, UK, July 9–13, 2018. Cham: Springer. Lect. Notes Comput. Sci. Eng. 134, 525-535 (2020). MSC: 65M60 65M06 65N30 76M10 76M20 35Q31 PDFBibTeX XMLCite \textit{H. Ranocha}, Lect. Notes Comput. Sci. Eng. 134, 525--535 (2020; Zbl 1484.65233) Full Text: DOI
Öffner, Philipp; Glaubitz, Jan; Ranocha, Hendrik Analysis of artificial dissipation of explicit and implicit time-integration methods. (English) Zbl 1471.65120 Int. J. Numer. Anal. Model. 17, No. 3, 332-349 (2020). MSC: 65M12 35L65 65M20 PDFBibTeX XMLCite \textit{P. Öffner} et al., Int. J. Numer. Anal. Model. 17, No. 3, 332--349 (2020; Zbl 1471.65120) Full Text: arXiv Link
Del Rey Fernández, David C.; Carpenter, Mark H.; Dalcin, Lisandro; Fredrich, Lucas; Winters, Andrew R.; Gassner, Gregor J.; Parsani, Matteo Entropy-stable \(p\)-nonconforming discretizations with the summation-by-parts property for the compressible Navier-Stokes equations. (English) Zbl 1521.76326 Comput. Fluids 210, Article ID 104631, 14 p. (2020). MSC: 76M10 65M60 76N06 PDFBibTeX XMLCite \textit{D. C. Del Rey Fernández} et al., Comput. Fluids 210, Article ID 104631, 14 p. (2020; Zbl 1521.76326) Full Text: DOI arXiv
Nolasco, Irving Reyna; Dalcin, Lisandro; Del Rey Fernández, David C.; Zampini, Stefano; Parsani, Matteo Optimized geometrical metrics satisfying free-stream preservation. (English) Zbl 1502.76079 Comput. Fluids 207, Article ID 104555, 16 p. (2020). MSC: 76M99 76Nxx 65M99 65Y20 PDFBibTeX XMLCite \textit{I. R. Nolasco} et al., Comput. Fluids 207, Article ID 104555, 16 p. (2020; Zbl 1502.76079) Full Text: DOI arXiv
Manzanero, Juan; Rubio, Gonzalo; Kopriva, David A.; Ferrer, Esteban; Valero, Eusebio A free-energy stable nodal discontinuous Galerkin approximation with summation-by-parts property for the Cahn-Hilliard equation. (English) Zbl 1453.65338 J. Comput. Phys. 403, Article ID 109072, 25 p. (2020). MSC: 65M60 65M12 PDFBibTeX XMLCite \textit{J. Manzanero} et al., J. Comput. Phys. 403, Article ID 109072, 25 p. (2020; Zbl 1453.65338) Full Text: DOI arXiv
Kriksin, Y. A.; Tishkin, V. F. Entropy stable discontinuous Galerkin method for Euler equations using non-conservative variables. (Russian. English summary) Zbl 1456.76073 Mat. Model. 32, No. 9, 87-102 (2020). MSC: 76M10 76N15 PDFBibTeX XMLCite \textit{Y. A. Kriksin} and \textit{V. F. Tishkin}, Mat. Model. 32, No. 9, 87--102 (2020; Zbl 1456.76073) Full Text: DOI MNR
Del Rey Fernández, David C.; Carpenter, Mark H.; Dalcin, Lisandro; Zampini, Stefano; Parsani, Matteo Entropy stable \(h/p\)-nonconforming discretization with the summation-by-parts property for the compressible Euler and Navier-Stokes equations. (English) Zbl 1454.65123 SN Partial Differ. Equ. Appl. 1, No. 2, Paper No. 9, 54 p. (2020). MSC: 65M70 65D05 65L06 65M12 65P40 65Z05 76N06 76L05 76F06 35Q30 PDFBibTeX XMLCite \textit{D. C. Del Rey Fernández} et al., SN Partial Differ. Equ. Appl. 1, No. 2, Paper No. 9, 54 p. (2020; Zbl 1454.65123) Full Text: DOI arXiv
Wen, Xiao; Don, Wai Sun; Gao, Zhen; Xing, Yulong Entropy stable and well-balanced discontinuous Galerkin methods for the nonlinear shallow water equations. (English) Zbl 1445.76055 J. Sci. Comput. 83, No. 3, Paper No. 66, 32 p. (2020). MSC: 76M12 76M20 76B15 86-08 PDFBibTeX XMLCite \textit{X. Wen} et al., J. Sci. Comput. 83, No. 3, Paper No. 66, 32 p. (2020; Zbl 1445.76055) Full Text: DOI
Wu, Kailiang; Shu, Chi-Wang Entropy symmetrization and high-order accurate entropy stable numerical schemes for relativistic MHD equations. (English) Zbl 1450.65089 SIAM J. Sci. Comput. 42, No. 4, A2230-A2261 (2020). Reviewer: Qifeng Zhang (Hangzhou) MSC: 65M06 65M12 76W05 76Y05 76M20 35L65 35Q35 PDFBibTeX XMLCite \textit{K. Wu} and \textit{C.-W. Shu}, SIAM J. Sci. Comput. 42, No. 4, A2230--A2261 (2020; Zbl 1450.65089) Full Text: DOI arXiv
Bragin, M. D.; Kriksin, Yu. A.; Tishkin, V. F. Discontinuous Galerkin method with entropic slope limiter for Euler equations. (Russian. English summary) Zbl 1444.76068 Mat. Model. 32, No. 2, 113-128 (2020). MSC: 76M10 76N15 PDFBibTeX XMLCite \textit{M. D. Bragin} et al., Mat. Model. 32, No. 2, 113--128 (2020; Zbl 1444.76068) Full Text: DOI MNR
Shadpey, Siavosh; Zingg, David W. Entropy-stable multidimensional summation-by-parts discretizations on hp-adaptive curvilinear grids for hyperbolic conservation laws. (English) Zbl 07197755 J. Sci. Comput. 82, No. 3, Paper No. 70, 46 p. (2020). MSC: 65Dxx 35Jxx 65Nxx PDFBibTeX XMLCite \textit{S. Shadpey} and \textit{D. W. Zingg}, J. Sci. Comput. 82, No. 3, Paper No. 70, 46 p. (2020; Zbl 07197755) Full Text: DOI
Glaubitz, Jan; Öffner, Philipp Stable discretisations of high-order discontinuous Galerkin methods on equidistant and scattered points. (English) Zbl 1434.65180 Appl. Numer. Math. 151, 98-118 (2020). MSC: 65M60 65M70 35L65 65D32 33C45 PDFBibTeX XMLCite \textit{J. Glaubitz} and \textit{P. Öffner}, Appl. Numer. Math. 151, 98--118 (2020; Zbl 1434.65180) Full Text: DOI arXiv Link
Del Rey Fernández, David C.; Crean, Jared; Carpenter, Mark H.; Hicken, Jason E. Staggered-grid entropy-stable multidimensional summation-by-parts discretizations on curvilinear coordinates. (English) Zbl 1452.76085 J. Comput. Phys. 392, 161-186 (2019). MSC: 76M10 65M60 PDFBibTeX XMLCite \textit{D. C. Del Rey Fernández} et al., J. Comput. Phys. 392, 161--186 (2019; Zbl 1452.76085) Full Text: DOI
Renac, Florent Entropy stable DGSEM for nonlinear hyperbolic systems in nonconservative form with application to two-phase flows. (English) Zbl 1451.76073 J. Comput. Phys. 382, 1-26 (2019). MSC: 76M10 76M22 65M60 65M70 76T10 65M12 35L45 PDFBibTeX XMLCite \textit{F. Renac}, J. Comput. Phys. 382, 1--26 (2019; Zbl 1451.76073) Full Text: DOI arXiv
Kriksin, Y. A.; Tishkin, V. F. Variational entropic regularization of discontinuous Galerkin method for gas dynamics equations. (Russian. English summary) Zbl 1442.35342 Mat. Model. 31, No. 5, 69-84 (2019). MSC: 35Q35 76N15 35A15 35B65 35L65 PDFBibTeX XMLCite \textit{Y. A. Kriksin} and \textit{V. F. Tishkin}, Mat. Model. 31, No. 5, 69--84 (2019; Zbl 1442.35342) Full Text: DOI MNR
Erickson, Brittany A.; O’Reilly, Ossian; Nordström, Jan Accuracy of stable, high-order finite difference methods for hyperbolic systems with non-smooth wave speeds. (English) Zbl 1447.65021 J. Sci. Comput. 81, No. 3, 2356-2387 (2019). Reviewer: Bülent Karasözen (Ankara) MSC: 65M06 65M12 35C05 44A10 PDFBibTeX XMLCite \textit{B. A. Erickson} et al., J. Sci. Comput. 81, No. 3, 2356--2387 (2019; Zbl 1447.65021) Full Text: DOI Link
Del Rey Fernández, David C.; Boom, Pieter D.; Carpenter, Mark H.; Zingg, David W. Extension of tensor-product generalized and dense-norm summation-by-parts operators to curvilinear coordinates. (English) Zbl 1428.65004 J. Sci. Comput. 80, No. 3, 1957-1996 (2019). MSC: 65M06 65M60 65M70 PDFBibTeX XMLCite \textit{D. C. Del Rey Fernández} et al., J. Sci. Comput. 80, No. 3, 1957--1996 (2019; Zbl 1428.65004) Full Text: DOI Link
Chang, Wei Shyang; Ismail, Farzad; Chizari, Hossain An entropy-stable residual distribution scheme for the system of two-dimensional inviscid shallow water equations. (English) Zbl 1422.65337 Bull. Malays. Math. Sci. Soc. (2) 42, No. 4, 1745-1771 (2019). MSC: 65N08 65N12 76B15 35Q35 PDFBibTeX XMLCite \textit{W. S. Chang} et al., Bull. Malays. Math. Sci. Soc. (2) 42, No. 4, 1745--1771 (2019; Zbl 1422.65337) Full Text: DOI
Friedrich, Lucas; Schnücke, Gero; Winters, Andrew R.; Fernández, David C. Del Rey; Gassner, Gregor J.; Carpenter, Mark H. Entropy stable space-time discontinuous Galerkin schemes with summation-by-parts property for hyperbolic conservation laws. (English) Zbl 1421.35262 J. Sci. Comput. 80, No. 1, 175-222 (2019). MSC: 35Q31 76B15 76N10 65M60 65M70 PDFBibTeX XMLCite \textit{L. Friedrich} et al., J. Sci. Comput. 80, No. 1, 175--222 (2019; Zbl 1421.35262) Full Text: DOI arXiv
Ranocha, Hendrik Mimetic properties of difference operators: product and chain rules as for functions of bounded variation and entropy stability of second derivatives. (English) Zbl 1482.65151 BIT 59, No. 2, 547-563 (2019). Reviewer: Anouar Ben Mabrouk (Sousse) MSC: 65M06 65M70 65N06 65N35 35L65 PDFBibTeX XMLCite \textit{H. Ranocha}, BIT 59, No. 2, 547--563 (2019; Zbl 1482.65151) Full Text: DOI arXiv
Yu, Hao; Wu, Boying; Zhang, Dazhi A generalized Laguerre spectral Petrov-Galerkin method for the time-fractional subdiffusion equation on the semi-infinite domain. (English) Zbl 1427.65311 Appl. Math. Comput. 331, 96-111 (2018). MSC: 65M70 35R11 65M15 PDFBibTeX XMLCite \textit{H. Yu} et al., Appl. Math. Comput. 331, 96--111 (2018; Zbl 1427.65311) Full Text: DOI
Wintermeyer, Niklas; Winters, Andrew R.; Gassner, Gregor J.; Warburton, Timothy An entropy stable discontinuous Galerkin method for the shallow water equations on curvilinear meshes with wet/dry fronts accelerated by GPUs. (English) Zbl 1416.65363 J. Comput. Phys. 375, 447-480 (2018). MSC: 65M60 76M10 86A05 86-08 65M12 65Y05 PDFBibTeX XMLCite \textit{N. Wintermeyer} et al., J. Comput. Phys. 375, 447--480 (2018; Zbl 1416.65363) Full Text: DOI arXiv Link
Abgrall, R. A general framework to construct schemes satisfying additional conservation relations. Application to entropy conservative and entropy dissipative schemes. (English) Zbl 1415.76442 J. Comput. Phys. 372, 640-666 (2018). MSC: 76M10 65N30 35L40 PDFBibTeX XMLCite \textit{R. Abgrall}, J. Comput. Phys. 372, 640--666 (2018; Zbl 1415.76442) Full Text: DOI arXiv Link
Winters, Andrew R.; Moura, Rodrigo C.; Mengaldo, Gianmarco; Gassner, Gregor J.; Walch, Stefanie; Peiro, Joaquim; Sherwin, Spencer J. A comparative study on polynomial dealiasing and split form discontinuous Galerkin schemes for under-resolved turbulence computations. (English) Zbl 1415.76461 J. Comput. Phys. 372, 1-21 (2018). MSC: 76M10 76M22 76B47 PDFBibTeX XMLCite \textit{A. R. Winters} et al., J. Comput. Phys. 372, 1--21 (2018; Zbl 1415.76461) Full Text: DOI arXiv
Derigs, Dominik; Gassner, Gregor J.; Walch, Stefanie; Winters, Andrew R. Entropy stable finite volume approximations for ideal magnetohydrodynamics. (English) Zbl 1447.78020 Jahresber. Dtsch. Math.-Ver. 120, No. 3, 153-219 (2018); correction ibid. 120, No. 4, 291-292 (2018). Reviewer: Balswaroop Bhatt (St. Augustine) MSC: 78M99 76W05 PDFBibTeX XMLCite \textit{D. Derigs} et al., Jahresber. Dtsch. Math.-Ver. 120, No. 3, 153--219 (2018; Zbl 1447.78020) Full Text: DOI arXiv Link
Chan, Jesse On discretely entropy conservative and entropy stable discontinuous Galerkin methods. (English) Zbl 1391.76310 J. Comput. Phys. 362, 346-374 (2018). MSC: 76M10 65M60 35L65 PDFBibTeX XMLCite \textit{J. Chan}, J. Comput. Phys. 362, 346--374 (2018; Zbl 1391.76310) Full Text: DOI arXiv
Ranocha, Hendrik Generalised summation-by-parts operators and variable coefficients. (English) Zbl 1395.65054 J. Comput. Phys. 362, 20-48 (2018). MSC: 65M12 35L65 35L60 PDFBibTeX XMLCite \textit{H. Ranocha}, J. Comput. Phys. 362, 20--48 (2018; Zbl 1395.65054) Full Text: DOI arXiv
Ranocha, Hendrik; Glaubitz, Jan; Öffner, Philipp; Sonar, Thomas Stability of artificial dissipation and modal filtering for flux reconstruction schemes using summation-by-parts operators. (English) Zbl 1404.65201 Appl. Numer. Math. 128, 1-23 (2018). MSC: 65M70 35L65 65M12 65D32 65M99 PDFBibTeX XMLCite \textit{H. Ranocha} et al., Appl. Numer. Math. 128, 1--23 (2018; Zbl 1404.65201) Full Text: DOI
Liu, Yong; Shu, Chi-Wang; Zhang, Mengping Entropy stable high order discontinuous Galerkin methods for ideal compressible MHD on structured meshes. (English) Zbl 1380.76162 J. Comput. Phys. 354, 163-178 (2018). MSC: 76W05 76M10 65M60 PDFBibTeX XMLCite \textit{Y. Liu} et al., J. Comput. Phys. 354, 163--178 (2018; Zbl 1380.76162) Full Text: DOI
Sun, Zheng; Carrillo, José A.; Shu, Chi-Wang A discontinuous Galerkin method for nonlinear parabolic equations and gradient flow problems with interaction potentials. (English) Zbl 1380.65287 J. Comput. Phys. 352, 76-104 (2018). MSC: 65M60 35Q84 PDFBibTeX XMLCite \textit{Z. Sun} et al., J. Comput. Phys. 352, 76--104 (2018; Zbl 1380.65287) Full Text: DOI arXiv
Ranocha, Hendrik Shallow water equations: split-form, entropy stable, well-balanced, and positivity preserving numerical methods. (English) Zbl 1432.65156 GEM. Int. J. Geomath. 8, No. 1, 85-133 (2017). MSC: 65M70 65M60 65M06 65M12 PDFBibTeX XMLCite \textit{H. Ranocha}, GEM. Int. J. Geomath. 8, No. 1, 85--133 (2017; Zbl 1432.65156) Full Text: DOI arXiv
Chen, Tianheng; Shu, Chi-Wang Entropy stable high order discontinuous Galerkin methods with suitable quadrature rules for hyperbolic conservation laws. (English) Zbl 1380.65253 J. Comput. Phys. 345, 427-461 (2017). MSC: 65M60 35L65 35D30 35R45 PDFBibTeX XMLCite \textit{T. Chen} and \textit{C.-W. Shu}, J. Comput. Phys. 345, 427--461 (2017; Zbl 1380.65253) Full Text: DOI
Ismail, Farzad; Chizari, Hossain Developments of entropy-stable residual distribution methods for conservation laws I: Scalar problems. (English) Zbl 1378.76082 J. Comput. Phys. 330, 1093-1115 (2017). MSC: 76M25 35L65 PDFBibTeX XMLCite \textit{F. Ismail} and \textit{H. Chizari}, J. Comput. Phys. 330, 1093--1115 (2017; Zbl 1378.76082) Full Text: DOI
Ranocha, Hendrik; Öffner, Philipp; Sonar, Thomas Extended skew-symmetric form for summation-by-parts operators and varying Jacobians. (English) Zbl 1380.65318 J. Comput. Phys. 342, 13-28 (2017). MSC: 65M99 35L65 35Q35 PDFBibTeX XMLCite \textit{H. Ranocha} et al., J. Comput. Phys. 342, 13--28 (2017; Zbl 1380.65318) Full Text: DOI arXiv
Wintermeyer, Niklas; Winters, Andrew R.; Gassner, Gregor J.; Kopriva, David A. An entropy stable nodal discontinuous Galerkin method for the two dimensional shallow water equations on unstructured curvilinear meshes with discontinuous bathymetry. (English) Zbl 1380.65291 J. Comput. Phys. 340, 200-242 (2017). MSC: 65M60 35Q35 65M70 PDFBibTeX XMLCite \textit{N. Wintermeyer} et al., J. Comput. Phys. 340, 200--242 (2017; Zbl 1380.65291) Full Text: DOI arXiv
Dumbser, Michael (ed.); Gassner, Gregor (ed.); Rohde, Christian (ed.); Roller, Sabine (ed.) Editorial: Preface to the special issue “Recent advances in numerical methods for hyperbolic partial differential equations”. (English) Zbl 1409.00105 Appl. Math. Comput. 272, Part 2, 235-236 (2016). MSC: 00B15 76-06 65-06 PDFBibTeX XMLCite \textit{M. Dumbser} (ed.) et al., Appl. Math. Comput. 272, Part 2, 235--236 (2016; Zbl 1409.00105) Full Text: DOI
Gassner, Gregor J.; Winters, Andrew R.; Kopriva, David A. Split form nodal discontinuous Galerkin schemes with summation-by-parts property for the compressible Euler equations. (English) Zbl 1422.65280 J. Comput. Phys. 327, 39-66 (2016). MSC: 65M70 65M60 76D05 35Q31 PDFBibTeX XMLCite \textit{G. J. Gassner} et al., J. Comput. Phys. 327, 39--66 (2016; Zbl 1422.65280) Full Text: DOI arXiv
Ranocha, Hendrik; Öffner, Philipp; Sonar, Thomas Summation-by-parts operators for correction procedure via reconstruction. (English) Zbl 1349.65524 J. Comput. Phys. 311, 299-328 (2016). MSC: 65M70 65M12 PDFBibTeX XMLCite \textit{H. Ranocha} et al., J. Comput. Phys. 311, 299--328 (2016; Zbl 1349.65524) Full Text: DOI arXiv
Winters, Andrew R.; Gassner, Gregor J. Affordable, entropy conserving and entropy stable flux functions for the ideal MHD equations. (English) Zbl 1349.76407 J. Comput. Phys. 304, 72-108 (2016). MSC: 76M12 65M08 76W05 PDFBibTeX XMLCite \textit{A. R. Winters} and \textit{G. J. Gassner}, J. Comput. Phys. 304, 72--108 (2016; Zbl 1349.76407) Full Text: DOI arXiv
Fambri, Francesco; Dumbser, Michael Spectral semi-implicit and space-time discontinuous Galerkin methods for the incompressible Navier-Stokes equations on staggered Cartesian grids. (English) Zbl 1432.76157 Appl. Numer. Math. 110, 41-74 (2016). MSC: 76M10 65M60 76D05 PDFBibTeX XMLCite \textit{F. Fambri} and \textit{M. Dumbser}, Appl. Numer. Math. 110, 41--74 (2016; Zbl 1432.76157) Full Text: DOI arXiv
Winters, Andrew R.; Gassner, Gregor J. An entropy stable finite volume scheme for the equations of shallow water magnetohydrodynamics. (English) Zbl 1381.76227 J. Sci. Comput. 67, No. 2, 514-539 (2016). MSC: 76M12 65M08 65M12 76W05 PDFBibTeX XMLCite \textit{A. R. Winters} and \textit{G. J. Gassner}, J. Sci. Comput. 67, No. 2, 514--539 (2016; Zbl 1381.76227) Full Text: DOI arXiv
Winters, Andrew R.; Gassner, Gregor J. A comparison of two entropy stable discontinuous Galerkin spectral element approximations for the shallow water equations with non-constant topography. (English) Zbl 1349.76285 J. Comput. Phys. 301, 357-376 (2015). MSC: 76M10 65M60 65M70 76D05 PDFBibTeX XMLCite \textit{A. R. Winters} and \textit{G. J. Gassner}, J. Comput. Phys. 301, 357--376 (2015; Zbl 1349.76285) Full Text: DOI Link