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Analysis and computation of a nonlinear Korteweg-de Vries system

Rincon, Mauro A. ; Xavier, Juliana C. ; Alfaro Vigo, Daniel G.

BIT, 2016-09, Vol.56 (3), p.1069-1099 [Periódico revisado por pares]

Dordrecht: Springer Netherlands

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Título:
Analysis and computation of a nonlinear Korteweg-de Vries system
Autor: Rincon, Mauro A. ; Xavier, Juliana C. ; Alfaro Vigo, Daniel G.
Assuntos: Basis functions ; Computational Mathematics and Numerical Analysis ; Computer simulation ; Dissipation ; Finite difference method ; Finite element method ; Functions (mathematics) ; Galerkin method ; Hermite polynomials ; Korteweg-Devries equation ; Mathematics ; Mathematics and Statistics ; Numeric Computing ; Numerical analysis ; Sobolev space ; Uniqueness ; Viscosity
É parte de: BIT, 2016-09, Vol.56 (3), p.1069-1099
Descrição: In this work, we present an analytical and numerical study of the Korteweg-de Vries (KdV) equation on a bounded domain in the presence of a dissipation mechanism. We present results on the existence and uniqueness of strong solutions using the Faedo–Galerkin method and studying a regularized version of the KdV equation. We also analyze the influence of this dissipation mechanism on the system energy. We introduce a numerical method based on a finite element discretization in space using Hermite polynomials as basis functions and the Crank–Nicolson finite difference scheme in time. Error estimates in Sobolev space for both the semi and fully-discrete problems are presented. Numerical simulations are also included in order to illustrate the applicability of the method. They also show the influence of the dissipative mechanism on the energy of the system.
Editor: Dordrecht: Springer Netherlands
Idioma: Inglês

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Analysis and computation of a nonlinear Korteweg-de Vries system

Rincon, Mauro A. ; Xavier, Juliana C. ; Alfaro Vigo, Daniel G.

Dordrecht: Springer Netherlands

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