Dissipative/conservative Galerkin method using discrete partial derivatives for nonlinear evolution equations

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:218

Article; Proceedings Paper

Matsuo, Takayasu

关键词: Galerkin method;    finite-element method;    conservation;    dissipation;    nonlinear Schrodinger equation;    Cahn-Hilliard equation;    Korteweg-de Vries equation;   

DOI  :  10.1016/j.cam.2007.08.001

来源: Elsevier

【 摘 要 】

Anew method is proposed for designing Galerkin schemes that retain the energy dissipation or conservation properties of nonlinear evolution equations such as the Cahn-Hilliard equation, the Korteweg-de Vries equation, or the nonlinear Schrodinger equation. In particular, as a special case, dissipative or conservative finite-element schemes can be derived. The key device there is the new concept of discrete partial derivatives. As examples of the application of the present method, dissipative or conservative Galerkin schemes are presented for the three equations with some numerical experiments. (c) 2007 Elsevier B.V. All rights reserved.

【 授权许可】

Free