Energy method for structure-preserving finite difference schemes and some properties of difference quotient

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:311

Article

Yoshikawa, Shuji¹ 

[1] Ehime Univ, Grad Sch Sci & Engn, Dept Engn Prod & Environm, Bunkyo Cho 3, Matsuyania, Ehime 7908577, Japan

关键词: Finite difference method;    Structure-preserving numerical method;    Cahn-Hilliard equation;    Boussinesq type equation;    Error estimate;    Existence of solution;   

DOI  :  10.1016/j.cam.2016.08.008

来源: Elsevier

【 摘 要 】

In this article we introduce the energy method for structure-preserving finite difference schemes which inherit the physical structures such as energy conservation or dissipative laws. Another aim is to give some useful properties for difference quotient which is compatible with the structure-preserving finite difference schemes. The method and properties enable us not only to take the problem with more general nonlinearity but also to improve proofs of error estimate between the numerical and exact solutions. Lastly we give two examples of application to the Cahn-Hilliard and the Boussinesq type equations. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

Free