A reduced Galerkin finite element formulation based on proper orthogonal decomposition for the generalized KDV-RLW-Rosenau equation

Journal of Inequalities and Applications

Research

Guang-Ri Piao¹  Wenju Zhao² 

[1] Department of Mathematics, Yanbian University, 133002, Yanji, Jilin, China;School of Mathematics, Shandong University, 25100, Jinan, Shandong, China;

关键词: Generalized KdV-RLW-Rosenau equation;    Proper orthogonal decomposition;    Quadratic B-spline Galerkin finite element method;    Crank-Nicolson method;    Error estimates;   

DOI  :  10.1186/s13660-023-03012-1

 received in 2023-05-03, accepted in 2023-07-13,  发布年份 2023

来源: Springer

【 摘 要 】

This paper investigates reduced-order modeling of the Korteweg de Vries regularized long-wave Rosenau (KdV-RLW-Rosenau) equation using semi- and fully-discrete B-spline Galerkin approximations. The approach involves the application of a proper orthogonal decomposition (POD) method to a Galerkin finite element (GFE) formulation, resulting in a POD GFE formulation with lower dimensions and high accuracy. The error between the reduced POD GFE solution and the traditional GFE solution is analyzed using the Crank-Nicolson method. Numerical examples show that the theoretical conclusions are consistent with the results of the numerical computation, and that the POD method is effective and feasible.

【 授权许可】

CC BY   
© Springer Nature Switzerland AG 2023

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