ERROR ESTIMATES FOR GALERKIN APPROXIMATIONS OF THE %26quot;CLASSICAL%26quot; BOUSSINESQ SYSTEM

作者：Antonopoulos D C^*; Dougalis V A

来源：Mathematics of Computation, 2013, 82(282): 689-717.

• Boussinesq systems
• nonlinear dispersive waves
• first-order hyperbolics
• Galerkin methods
• error estimates

We consider the %26quot;classical%26quot; Boussinesq system in one space dimension and its symmetric analog. These systems model two-way propagation of nonlinear, dispersive long waves of small amplitude on the surface of an ideal fluid in a uniform horizontal channel. We discretize an initial-boundary-value problem for these systems in space using Galerkin-finite element methods and prove error estimates for the resulting semidiscrete problems and also for their fully discrete analogs effected by explicit Runge-Kutta time-stepping procedures. The theoretical orders of convergence obtained are consistent with the results of numerical experiments that are also presented.

• 出版日期2013-4