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). The authors develop a related kernel analysis and constructive computational approach for the shallow-water (SW) system in which the properties of the kernel of the associated discretized problem are used to determine the presence and number of different type of spurious solutions. This matrix kernel scheme is computed using MATLAB and applied to investigate the presence, number, and structure of spurious modes arising in typical finite deference and finite element schemes. The kernel concept is then used to characterize the smallest representable vortices for several representative discrete finite difference and finite element schemes. Both uniform and unstructured mesh situations are considered and compared. Numerical experiments are consistent with the analytic results. Reviewer: Qin Mengzhao (Beijing) Cited in 10 Documents MSC: 35A35 Theoretical approximation in context of PDEs 76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction 76B47 Vortex flows for incompressible inviscid fluids 76B65 Rossby waves (MSC2010) 74S20 Finite difference methods applied to problems in solid mechanics 74S05 Finite element methods applied to problems in solid mechanics 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs Keywords:Rossby waves; vortex flows; unstructed mesh Software:Matlab PDFBibTeX XMLCite \textit{V. Rostand} et al., SIAM J. Sci. Comput. 31, No. 1, 531--556 (2008; Zbl 1191.35025) Full Text: DOI