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In this paper we consider the one-parameter family of Bona-Smith systems, which belongs to the class of Boussinesq systems modelling two-way propagation of long waves of small amplitude on the surface of water in a channel. We study three initial-boundary-value problems for these systems, corresponding, respectively, to nonhomogeneous Dirichlet, reflection,… (More)

- D. C. Antonopoulos, V. A. Dougalis
- Math. Comput.
- 2013

- D. C. Antonopoulos, V. A. Dougalis
- Mathematics and Computers in Simulation
- 2012

We consider the 'classical' Boussinesq system of water wave theory, which belongs to the class of Boussinesq systems modelling two-way propagation of long waves of small amplitude on the surface of water in a horizontal channel. (We also consider its completely symmetric analog). We discretize the initial-boundary-value problem for these systems,… (More)

We consider the periodic initial-value problem for the family of a-b-c-d Boussinesq systems, [8], [9], and their completely symmetric analogs, [10]. We approximate their solutions by the standard Galerkin-finite element method using smooth periodic splines for discretizing in space. We prove optimal-order L 2 error estimates for the resulting… (More)

In this paper we consider the one-parameter family of Bona-Smith systems, which belongs to the class of Boussinesq systems modelling two-way propagation of long waves of small amplitude on the surface of water in a channel. We study numerically three initial-boundary-value problems for these systems, corresponding, respectively, to homogeneous Dirichlet,… (More)

- D. C. Antonopoulos, V. A. Dougalis
- Math. Comput.
- 2016

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