Error estimates for Galerkin approximations of the 'classical' Boussinesq system

Autor:	D. C. Antonopoulos, Vassilios A. Dougalis
Rok vydání:	2012
Předmět:	Algebra and Number Theory Discretization Approximations of π Applied Mathematics Perfect fluid Small amplitude Mathematics::Numerical Analysis Computational Mathematics Nonlinear system Calculus Applied mathematics Kondratiev wave Boussinesq approximation (water waves) Galerkin method Mathematics
Zdroj:	Mathematics of Computation. 82:689-717
ISSN:	1088-6842 0025-5718
DOI:	10.1090/s0025-5718-2012-02663-9
Popis:	We consider the ‘classical’ 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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::772a3130367cb6794c1adc6828630854 https://doi.org/10.1090/s0025-5718-2012-02663-9 Zobrazit plný text záznamu