Arrutselvi, M.; Natarajan, E. Virtual element stabilization for the system of time-dependent nonlinear convection-diffusion-reaction equations. (English) Zbl 07691990 Comput. Math. Appl. 142, 121-139 (2023). MSC: 65N30 65N12 65N15 65M60 65M12 PDFBibTeX XMLCite \textit{M. Arrutselvi} and \textit{E. Natarajan}, Comput. Math. Appl. 142, 121--139 (2023; Zbl 07691990) Full Text: DOI
Beljadid, Abdelaziz; LeFloch, Philippe G.; Mohammadian, Abdolmajid Late-time asymptotic behavior of solutions to hyperbolic conservation laws on the sphere. (English) Zbl 1441.58015 Comput. Methods Appl. Mech. Eng. 349, 285-311 (2019). MSC: 58J70 35B40 35L65 65M08 PDFBibTeX XMLCite \textit{A. Beljadid} et al., Comput. Methods Appl. Mech. Eng. 349, 285--311 (2019; Zbl 1441.58015) Full Text: DOI
Peixoto, Pedro S.; Schreiber, Martin Semi-Lagrangian exponential integration with application to the rotating shallow water equations. (English) Zbl 1428.65057 SIAM J. Sci. Comput. 41, No. 5, B903-B928 (2019). MSC: 65M99 65N99 76U05 76B15 86A10 PDFBibTeX XMLCite \textit{P. S. Peixoto} and \textit{M. Schreiber}, SIAM J. Sci. Comput. 41, No. 5, B903--B928 (2019; Zbl 1428.65057) Full Text: DOI arXiv
Lozovskiy, Alexander; Farthing, Matthew; Kees, Chris Evaluation of Galerkin and Petrov-Galerkin model reduction for finite element approximations of the shallow water equations. (English) Zbl 1439.76086 Comput. Methods Appl. Mech. Eng. 318, 537-571 (2017). MSC: 76M10 65M60 76B15 PDFBibTeX XMLCite \textit{A. Lozovskiy} et al., Comput. Methods Appl. Mech. Eng. 318, 537--571 (2017; Zbl 1439.76086) Full Text: DOI
Gaudreault, Stéphane; Pudykiewicz, Janusz A. An efficient exponential time integration method for the numerical solution of the shallow water equations on the sphere. (English) Zbl 1351.76106 J. Comput. Phys. 322, 827-848 (2016). MSC: 76M12 65M20 65L04 65M08 76B15 86A05 PDFBibTeX XMLCite \textit{S. Gaudreault} and \textit{J. A. Pudykiewicz}, J. Comput. Phys. 322, 827--848 (2016; Zbl 1351.76106) Full Text: DOI
Peixoto, Pedro S. Accuracy analysis of mimetic finite volume operators on geodesic grids and a consistent alternative. (English) Zbl 1349.76376 J. Comput. Phys. 310, 127-160 (2016). MSC: 76M12 86-08 65M08 76B15 86A05 86A10 PDFBibTeX XMLCite \textit{P. S. Peixoto}, J. Comput. Phys. 310, 127--160 (2016; Zbl 1349.76376) Full Text: DOI
Katta, Kiran K.; Nair, Ramachandran D.; Kumar, Vinod High-order finite volume shallow water model on the cubed-sphere: 1D reconstruction scheme. (English) Zbl 1410.76237 Appl. Math. Comput. 266, 316-327 (2015). MSC: 76M12 65M08 65M50 76B15 86A05 PDFBibTeX XMLCite \textit{K. K. Katta} et al., Appl. Math. Comput. 266, 316--327 (2015; Zbl 1410.76237) Full Text: DOI
Cotter, C. J.; Thuburn, J. A finite element exterior calculus framework for the rotating shallow-water equations. (English) Zbl 1351.76054 J. Comput. Phys. 257, Part B, 1506-1526 (2014). MSC: 76M10 65M60 58A10 76B15 PDFBibTeX XMLCite \textit{C. J. Cotter} and \textit{J. Thuburn}, J. Comput. Phys. 257, Part B, 1506--1526 (2014; Zbl 1351.76054) Full Text: DOI arXiv Link
Sjögreen, Björn High order finite difference and finite volume methods for advection on the sphere. (English) Zbl 1252.65145 J. Sci. Comput. 51, No. 3, 703-732 (2012). MSC: 65M06 65M08 35L60 65M12 86A10 PDFBibTeX XMLCite \textit{B. Sjögreen}, J. Sci. Comput. 51, No. 3, 703--732 (2012; Zbl 1252.65145) Full Text: DOI
Ringler, T. D.; Thuburn, J.; Klemp, J. B.; Skamarock, W. C. A unified approach to energy conservation and potential vorticity dynamics for arbitrarily-structured C-grids. (English) Zbl 1307.76054 J. Comput. Phys. 229, No. 9, 3065-3090 (2010). MSC: 76M12 76B15 65M08 65M50 PDFBibTeX XMLCite \textit{T. D. Ringler} et al., J. Comput. Phys. 229, No. 9, 3065--3090 (2010; Zbl 1307.76054) Full Text: DOI Link
Liu, Biyue An error analysis of a finite element method for a system of nonlinear advection-diffusion-reaction equations. (English) Zbl 1169.65085 Appl. Numer. Math. 59, No. 8, 1947-1959 (2009). Reviewer: Răzvan Răducanu (Iaşi) MSC: 65M15 65M60 35K57 PDFBibTeX XMLCite \textit{B. Liu}, Appl. Numer. Math. 59, No. 8, 1947--1959 (2009; Zbl 1169.65085) Full Text: DOI
Skiba, Yuri N.; Filatov, Denis M. Conservative arbitrary order finite difference schemes for shallow-water flows. (English) Zbl 1225.76216 J. Comput. Appl. Math. 218, No. 2, 579-591 (2008). MSC: 76M20 76B15 65M06 PDFBibTeX XMLCite \textit{Y. N. Skiba} and \textit{D. M. Filatov}, J. Comput. Appl. Math. 218, No. 2, 579--591 (2008; Zbl 1225.76216) Full Text: DOI
Rossmanith, James A. A wave propagation method for hyperbolic systems on the sphere. (English) Zbl 1089.65088 J. Comput. Phys. 213, No. 2, 629-658 (2006). MSC: 65M06 35L45 76M12 76B15 76W05 PDFBibTeX XMLCite \textit{J. A. Rossmanith}, J. Comput. Phys. 213, No. 2, 629--658 (2006; Zbl 1089.65088) Full Text: DOI
Giraldo, Francis X. High-order triangle-based discontinuous Galerkin methods for hyperbolic equations on a rotating sphere. (English) Zbl 1089.65096 J. Comput. Phys. 214, No. 2, 447-465 (2006). MSC: 65M60 65M06 35L65 76B15 76M12 76M10 PDFBibTeX XMLCite \textit{F. X. Giraldo}, J. Comput. Phys. 214, No. 2, 447--465 (2006; Zbl 1089.65096) Full Text: DOI
Giraldo, F. X.; Warburton, T. A nodal triangle-based spectral element method for the shallow water equations on the sphere. (English) Zbl 1177.86002 J. Comput. Phys. 207, No. 1, 129-150 (2005). MSC: 86-08 86A05 76M10 76U05 65M60 PDFBibTeX XMLCite \textit{F. X. Giraldo} and \textit{T. Warburton}, J. Comput. Phys. 207, No. 1, 129--150 (2005; Zbl 1177.86002) Full Text: DOI
St-Cyr, Amik; Thomas, Stephen J. Nonlinear operator integration factor splitting for the shallow water equations. (English) Zbl 1142.76430 Appl. Numer. Math. 52, No. 4, 429-448 (2005). MSC: 76M22 76B15 65M99 65L99 PDFBibTeX XMLCite \textit{A. St-Cyr} and \textit{S. J. Thomas}, Appl. Numer. Math. 52, No. 4, 429--448 (2005; Zbl 1142.76430) Full Text: DOI
Rossmanith, James A.; Bale, Derek S.; LeVeque, Randall J. A wave propagation algorithm for hyperbolic systems on curved manifolds. (English) Zbl 1126.76350 J. Comput. Phys. 199, No. 2, 631-662 (2004). MSC: 76M25 65M06 35L60 86-08 PDFBibTeX XMLCite \textit{J. A. Rossmanith} et al., J. Comput. Phys. 199, No. 2, 631--662 (2004; Zbl 1126.76350) Full Text: DOI Link
Layton, Anita T.; Spotz, William F. A semi-Lagrangian double Fourier method for the shallow water equations on the sphere. (English) Zbl 1097.86003 J. Comput. Phys. 189, No. 1, 180-196 (2003). MSC: 86A10 65M70 76B15 76M25 86-08 PDFBibTeX XMLCite \textit{A. T. Layton} and \textit{W. F. Spotz}, J. Comput. Phys. 189, No. 1, 180--196 (2003; Zbl 1097.86003) Full Text: DOI
Göttelmann, Jochen A spine collocation scheme for the spherical shallow water equations. (English) Zbl 0947.76065 J. Comput. Phys. 148, No. 1, 291-298 (1999). MSC: 76M25 76B15 65M20 76U05 86A05 86A10 PDFBibTeX XMLCite \textit{J. Göttelmann}, J. Comput. Phys. 148, No. 1, 291--298 (1999; Zbl 0947.76065) Full Text: DOI
Stuhne, G. R.; Peltier, W. R. New icosahedral grid-point discretizations of the shallow water equations on the sphere. (English) Zbl 0930.76067 J. Comput. Phys. 148, No. 1, 23-58 (1999). MSC: 76M25 76B15 65M55 PDFBibTeX XMLCite \textit{G. R. Stuhne} and \textit{W. R. Peltier}, J. Comput. Phys. 148, No. 1, 23--58 (1999; Zbl 0930.76067) Full Text: DOI Link
Spotz, William F.; Taylor, Mark A.; Swarztrauber, Paul N. Fast shallow-water equation solvers in latitude-longitude coordinates. (English) Zbl 0928.76078 J. Comput. Phys. 145, No. 1, 432-444 (1998). MSC: 76M22 76B15 76U05 65M70 PDFBibTeX XMLCite \textit{W. F. Spotz} et al., J. Comput. Phys. 145, No. 1, 432--444 (1998; Zbl 0928.76078) Full Text: DOI