Analytical and Rothe time-discretization method for a Boussinesq-type system over an uneven bottom. (English) Zbl 1472.65113
The authors consider the analytical and numerical resolution of a 2D version of a Boussinesq-type model which occur in the water wave propagation. The time discretization is performed using a finite-difference second-order Crank-Nicholson-type scheme, and then, at each time step, the spatial variables are discretized with an efficient Galerkin/Finite Element Method (FEM) using triangular-finite elements based on 2D piecewise-linear Lagrange interpolation. Some numerical tests are presented to support the theoretical results.
Reviewer: Abdallah Bradji (Annaba)
MSC:
| 65M22 | Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs |
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 76B15 | Water waves, gravity waves; dispersion and scattering, nonlinear interaction |
| 76B25 | Solitary waves for incompressible inviscid fluids |
| 35Q35 | PDEs in connection with fluid mechanics |
Keywords:
Boussinesq-type system; moving bathymetry; finite element method; Crank-Nicholson-type schemeReferences:
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