Lin, Shuning; Chen, Yong Gradient-enhanced physics-informed neural networks based on transfer learning for inverse problems of the variable coefficient differential equations. (English) Zbl 07814534 Physica D 459, Article ID 134023, 21 p. (2024). MSC: 35Q55 35Q41 35R30 35C08 68T07 78A60 76U65 65K10 65M99 35R60 PDFBibTeX XMLCite \textit{S. Lin} and \textit{Y. Chen}, Physica D 459, Article ID 134023, 21 p. (2024; Zbl 07814534) Full Text: DOI arXiv
Crisan, D.; Holm, D. D.; Luesink, E.; Mensah, P. R.; Pan, W. Theoretical and computational analysis of the thermal quasi-geostrophic model. (English) Zbl 07741969 J. Nonlinear Sci. 33, No. 5, Paper No. 96, 58 p. (2023). MSC: 35Q86 35Q31 76U60 76U65 76R10 76M60 65D30 65M60 65M06 65L06 65N30 65M12 35D35 35B65 86A05 PDFBibTeX XMLCite \textit{D. Crisan} et al., J. Nonlinear Sci. 33, No. 5, Paper No. 96, 58 p. (2023; Zbl 07741969) Full Text: DOI arXiv
Girfoglio, Michele; Quaini, Annalisa; Rozza, Gianluigi A novel large eddy simulation model for the quasi-geostrophic equations in a finite volume setting. (English) Zbl 1502.65088 J. Comput. Appl. Math. 418, Article ID 114656, 13 p. (2023). MSC: 65M08 65M06 65N08 65M12 86A05 76U60 76U65 76F65 76M12 86-08 35Q35 35Q86 PDFBibTeX XMLCite \textit{M. Girfoglio} et al., J. Comput. Appl. Math. 418, Article ID 114656, 13 p. (2023; Zbl 1502.65088) Full Text: DOI arXiv
Bourne, David P.; Egan, Charlie P.; Pelloni, Beatrice; Wilkinson, Mark Semi-discrete optimal transport methods for the semi-geostrophic equations. (English) Zbl 1509.35318 Calc. Var. Partial Differ. Equ. 61, No. 1, Paper No. 39, 34 p. (2022). MSC: 35Q86 35Q49 86A10 76U65 76D05 35A01 35A35 35D30 35B65 35A24 65L06 65M12 65K10 52C22 49Q22 PDFBibTeX XMLCite \textit{D. P. Bourne} et al., Calc. Var. Partial Differ. Equ. 61, No. 1, Paper No. 39, 34 p. (2022; Zbl 1509.35318) Full Text: DOI arXiv
Chen, Qingshan; Ju, Lili; Temam, Roger Conservative numerical schemes with optimal dispersive wave relations: part I. Derivation and analysis. (English) Zbl 1477.35273 Numer. Math. 149, No. 1, 43-85 (2021). MSC: 35Q86 35Q35 76B47 76U60 76U65 86A05 65M08 65P10 86-08 PDFBibTeX XMLCite \textit{Q. Chen} et al., Numer. Math. 149, No. 1, 43--85 (2021; Zbl 1477.35273) Full Text: DOI arXiv
Fu, Lei; Zhang, Heng; He, Hailun; Dong, Huanhe; Yang, Hongwei Effect of nonlinearity on interaction between the vortices in the f-plane shallow water system. (English) Zbl 1476.35281 Z. Angew. Math. Phys. 72, No. 4, Paper No. 144, 18 p. (2021). MSC: 35Q86 35Q35 35Q51 35B40 35C08 76B47 76U60 76U65 86A05 35R35 65H10 65M70 65N30 PDFBibTeX XMLCite \textit{L. Fu} et al., Z. Angew. Math. Phys. 72, No. 4, Paper No. 144, 18 p. (2021; Zbl 1476.35281) Full Text: DOI
Chertock, Alina; Dudzinski, Michael; Kurganov, Alexander; Lukáčová-Medvid’ová, Mária Well-balanced schemes for the shallow water equations with Coriolis forces. (English) Zbl 1448.65097 Numer. Math. 138, No. 4, 939-973 (2018). MSC: 65M06 65N08 35L45 35L65 65M25 65M15 76B15 76U60 76U65 35Q86 86A05 65J10 PDFBibTeX XMLCite \textit{A. Chertock} et al., Numer. Math. 138, No. 4, 939--973 (2018; Zbl 1448.65097) Full Text: DOI
Balk, Alexander M. Rossby wave extra invariant in the Galerkin approximation. (English) Zbl 1375.76211 Phys. Lett., A 381, No. 31, 2510-2513 (2017). MSC: 76W05 65L60 82D10 76E25 PDFBibTeX XMLCite \textit{A. M. Balk}, Phys. Lett., A 381, No. 31, 2510--2513 (2017; Zbl 1375.76211) Full Text: DOI
Duarte, Rui; Carton, Xavier; Poulin, Francis J. The dynamics of a meandering coastal jet in the lee of a cape. (English) Zbl 1344.86004 Regul. Chaotic Dyn. 21, No. 3, 274-290 (2016). MSC: 86A05 65Z05 76U05 76E20 76E30 PDFBibTeX XMLCite \textit{R. Duarte} et al., Regul. Chaotic Dyn. 21, No. 3, 274--290 (2016; Zbl 1344.86004) Full Text: DOI
Beljadid, Abdelaziz; Mohammadian, Abdolmajid; Qiblawey, Hazim M. An unstructured finite volume method for large-scale shallow flows using the fourth-order Adams scheme. (English) Zbl 1390.86004 Comput. Fluids 88, 579-589 (2013). MSC: 86-08 76M12 86A10 65M08 76D05 86A05 PDFBibTeX XMLCite \textit{A. Beljadid} et al., Comput. Fluids 88, 579--589 (2013; Zbl 1390.86004) Full Text: DOI
Beljadid, A.; Mohammadian, A.; Qiblawey, Hazim Numerical simulation of rotation dominated linear shallow water flows using finite volume methods and fourth order Adams scheme. (English) Zbl 1365.76137 Comput. Fluids 62, 64-70 (2012). MSC: 76M12 76U05 76B15 65M08 65L06 PDFBibTeX XMLCite \textit{A. Beljadid} et al., Comput. Fluids 62, 64--70 (2012; Zbl 1365.76137) Full Text: DOI
Yang, Hong-Wei; Yin, Bao-Shu; Dong, Huan-He; Shi, Yun-Long Algebraic Rossby solitary waves excited by non-stationary external source. (English) Zbl 1264.76030 Commun. Theor. Phys. 58, No. 3, 425-431 (2012). MSC: 76B65 76B47 76E20 76M22 35Q53 35C08 35L65 65M70 PDFBibTeX XMLCite \textit{H.-W. Yang} et al., Commun. Theor. Phys. 58, No. 3, 425--431 (2012; Zbl 1264.76030) Full Text: DOI
Cotter, C. J.; Ham, D. A. Numerical wave propagation for the triangular \(P1_{DG}-P2\) finite element pair. (English) Zbl 1316.76019 J. Comput. Phys. 230, No. 8, 2806-2820 (2011). MSC: 76B15 65N30 76M10 86A10 PDFBibTeX XMLCite \textit{C. J. Cotter} and \textit{D. A. Ham}, J. Comput. Phys. 230, No. 8, 2806--2820 (2011; Zbl 1316.76019) Full Text: DOI arXiv
Ferguson, James; Khouider, Boualem; Namazi, Maryam Two-way interactions between equatorially-trapped waves and the barotropic flow. (English) Zbl 1261.86004 Chin. Ann. Math., Ser. B 30, No. 5, 539-568 (2009). MSC: 86A10 76B15 76B55 76B60 65M06 PDFBibTeX XMLCite \textit{J. Ferguson} et al., Chin. Ann. Math., Ser. B 30, No. 5, 539--568 (2009; Zbl 1261.86004) Full Text: DOI
Rostand, Virgile; Le Roux, Daniel Y.; Carey, Graham Kernel analysis of the discretized finite difference and finite element shallow-water models. (English) Zbl 1191.35025 SIAM J. Sci. Comput. 31, No. 1, 531-556 (2008). Reviewer: Qin Mengzhao (Beijing) MSC: 35A35 76B15 76B47 76B65 74S20 74S05 65M06 PDFBibTeX XMLCite \textit{V. Rostand} et al., SIAM J. Sci. Comput. 31, No. 1, 531--556 (2008; Zbl 1191.35025) Full Text: DOI
Le Roux, Daniel Y.; Pouliot, Benoit Analysis of numerically induced oscillations in two-dimensional finite-element shallow-water models. II: Free planetary waves. (English) Zbl 1191.35024 SIAM J. Sci. Comput. 30, No. 4, 1971-1991 (2008). Reviewer: Argiris I. Delis (Chania) MSC: 35A35 65L60 76B65 65M60 PDFBibTeX XMLCite \textit{D. Y. Le Roux} and \textit{B. Pouliot}, SIAM J. Sci. Comput. 30, No. 4, 1971--1991 (2008; Zbl 1191.35024) Full Text: DOI
Thuburn, J. Numerical wave propagation on the hexagonal C-grid. (English) Zbl 1220.76018 J. Comput. Phys. 227, No. 11, 5836-5858 (2008). MSC: 76B15 65M12 76U05 86A05 PDFBibTeX XMLCite \textit{J. Thuburn}, J. Comput. Phys. 227, No. 11, 5836--5858 (2008; Zbl 1220.76018) Full Text: DOI Link
Smith, Robert K.; Dritschel, David G. Revisiting the Rossby-Haurwitz wave test case with contour advection. (English) Zbl 1160.86305 J. Comput. Phys. 217, No. 2, 473-484 (2006). MSC: 86A10 65M06 76B65 86A05 PDFBibTeX XMLCite \textit{R. K. Smith} and \textit{D. G. Dritschel}, J. Comput. Phys. 217, No. 2, 473--484 (2006; Zbl 1160.86305) Full Text: DOI
Layton, Anita T.; Christara, Christina C.; Jackson, Kenneth R. Quadratic spline methods for the shallow water equations on the sphere: Collocation. (English) Zbl 1161.76514 Math. Comput. Simul. 71, No. 3, 187-205 (2006). MSC: 76M10 65M60 76B15 76B65 86A05 PDFBibTeX XMLCite \textit{A. T. Layton} et al., Math. Comput. Simul. 71, No. 3, 187--205 (2006; Zbl 1161.76514) Full Text: DOI
Layton, Anita T.; Christara, Christina C.; Jackson, Kenneth R. Quadratic spline methods for the shallow water equations on the sphere: Galerkin. (English) Zbl 1161.76029 Math. Comput. Simul. 71, No. 3, 175-186 (2006). MSC: 76M10 65M60 76B15 76B65 86A05 PDFBibTeX XMLCite \textit{A. T. Layton} et al., Math. Comput. Simul. 71, No. 3, 175--186 (2006; Zbl 1161.76029) Full Text: DOI
Skiba, Yuri N.; Pérez-García, Ismael On the structure and growth rate of unstable modes to the Rossby-Haurwitz wave. (English) Zbl 1141.76391 Numer. Methods Partial Differ. Equations 21, No. 2, 368-386 (2005). MSC: 76E20 65M70 76B60 76B65 76U05 86A10 PDFBibTeX XMLCite \textit{Y. N. Skiba} and \textit{I. Pérez-García}, Numer. Methods Partial Differ. Equations 21, No. 2, 368--386 (2005; Zbl 1141.76391) Full Text: DOI
Kaladze, T.; Rogava, J.; Tsamalashvili, L.; Tsiklauri, M. First- and second-order accurate implicit difference schemes for the Charney-Obukhov equation. (English) Zbl 1134.76408 Phys. Lett., A 328, No. 1, 51-64 (2004). MSC: 76M20 65M06 76B65 86-08 PDFBibTeX XMLCite \textit{T. Kaladze} et al., Phys. Lett., A 328, No. 1, 51--64 (2004; Zbl 1134.76408) Full Text: DOI
Yavneh, Irad; McWilliams, James C. Robust multigrid solution of the shallow water balance equations. (English) Zbl 0919.76063 J. Comput. Phys. 119, No. 1, 1-25 (1995). MSC: 76M20 76B65 86A05 65M55 PDFBibTeX XMLCite \textit{I. Yavneh} and \textit{J. C. McWilliams}, J. Comput. Phys. 119, No. 1, 1--25 (1995; Zbl 0919.76063) Full Text: DOI
Ma, Hong A spectral element basin model for the shallow water equations. (English) Zbl 0790.76065 J. Comput. Phys. 109, No. 1, 133-149 (1993). MSC: 76M25 76B15 65M70 86A05 PDFBibTeX XMLCite \textit{H. Ma}, J. Comput. Phys. 109, No. 1, 133--149 (1993; Zbl 0790.76065) Full Text: DOI Link
Zou, X.; Navon, I. M.; Berger, M.; Phua, K. H.; Schlick, T.; Le Dimet, F. X. Numerical experience with limited-memory quasi-Newton and truncated Newton methods. (English) Zbl 0784.90086 SIAM J. Optim. 3, No. 3, 582-608 (1993). MSC: 90C30 90-08 65K05 93C20 93C95 65K10 76B65 90C06 PDFBibTeX XMLCite \textit{X. Zou} et al., SIAM J. Optim. 3, No. 3, 582--608 (1993; Zbl 0784.90086) Full Text: DOI Link
Zhong, Qing The formulation of a perfect square conservative semi-implicit time difference scheme and its preliminary check. (English) Zbl 0758.65080 Chin. Sci. Bull. 37, No. 6, 497-502 (1992). Reviewer: K.T.S.R.Iyengar (Bangalore) MSC: 65Z05 65M06 65M12 86A10 76B60 PDFBibTeX XMLCite \textit{Q. Zhong}, Chin. Sci. Bull. 37, No. 6, 497--502 (1992; Zbl 0758.65080)
Wang, Bin; Ji, Zhongzhen The construction and preliminary test of the explicit complete square conservative difference schemes. (English) Zbl 0736.65067 Chin. Sci. Bull. 35, No. 20, 1724-1728 (1990). Reviewer: K.T.S.R.Iyengar (Bangalore) MSC: 65M06 35K15 76B65 PDFBibTeX XMLCite \textit{B. Wang} and \textit{Z. Ji}, Chin. Sci. Bull. 35, No. 20, 1724--1728 (1990; Zbl 0736.65067)
Kinnmark, I. The shallow water wave equations: formulation, analysis and application. (English) Zbl 0588.76001 Lecture Notes in Engineering, 15. Berlin etc.: Springer-Verlag. XXV, 187 p. DM 39.00 (1986). Reviewer: H.F.Bauer MSC: 76-02 76B15 86A05 65N06 76M99 76B65 PDFBibTeX XML
Bates, J. R. Semi-Lagrangian advective schemes and their use in meteorological modeling. (English) Zbl 0589.76041 Large-scale computations in fluid mechanics, Proc. 15th AMS-SIAM Summer Semin. Appl. Math., La Jolla/Calif. 1983, Lect. Appl. Math. 22, Pt. 1, 1-29 (1985). Reviewer: B.Fisher MSC: 76B65 76M99 86A99 76B15 65C20 PDFBibTeX XML
Rhines, Peter B. Geostrophic turbulence. (English) Zbl 0474.76054 Annu. Rev. Fluid Mech. 11, 401-441 (1979). MSC: 76F99 76B47 86A05 76B65 65Z05 49S05 82B99 PDFBibTeX XML
Mesinger, F. Dependence of vorticity analogue and the Rossby wave phase speed on the choice of horizontal grid. (English) Zbl 0425.76022 Bull., Cl. Sci. Math. Nat., Sci. Math., Nouv. Ser. No. 10, 5-15 (1979). MSC: 76B47 76B65 65C20 86A99 PDFBibTeX XML
Sheshukov, E. G. An approximative-analogous method for solving problems of nonlinear filtration. (Russian) Zbl 0442.76022 Tr. Semin. Kraev. Zadacham 15, 168-175 (1978). MSC: 76B65 65C99 PDFBibTeX XMLCite \textit{E. G. Sheshukov}, Tr. Semin. Kraev. Zadacham 15, 168--175 (1978; Zbl 0442.76022) Full Text: EuDML
Volosov, V. M. Topographic waves in rotating layer of liquid. (Russian) Zbl 0414.76020 Probl. asympt. Theory nonlin. Oscill., Acad. Sci. Ukr. SSR, Inst. Math., 71-76 (1977). MSC: 76B65 65L99 35E05 PDFBibTeX XML
Talagrand, O.; Anderson, D.; Ghil, M. Éléments de meteorologie dynamique. (French) Zbl 0365.76046 Fluid Dyn., Summer Sch. theor. Phys., Les Houches 1973, 641-656 (1977). MSC: 76E25 76B65 65-02 PDFBibTeX XML
Steppeler, J. On the problem of boundary conditions in primitive equation models. (English) Zbl 0339.76015 Contrib. Atmos. Phys. 49, 43-54 (1976). MSC: 76B65 39A10 65Q05 PDFBibTeX XMLCite \textit{J. Steppeler}, Contrib. Atmos. Phys. 49, 43--54 (1976; Zbl 0339.76015)
Fix, George Finite elements and fluid dynamics. (English) Zbl 0311.76017 Comput. Mech., int. Conf. comput. Meth. nonlin. Mech., Austin 1974, Lect. Notes Math. 461, 47-70 (1975). MSC: 76E05 76B47 76D05 76B65 65N30 PDFBibTeX XML