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Kernel analysis of the discretized finite difference and finite element shallow-water models. (English) Zbl 1191.35025
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.

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
Software:
Matlab
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