Finite difference-finite element approach for solving fractional Oldroyd-B equation

Advances in Difference Equations

Abdul Wahab¹  Shaista Qaim Shah²  Rab Nawaz³  Amer Rasheed⁴ 

[1] Bio-imaging and Signal Processing Lab., Department of Bio and Brain Engineering, Korea Advanced Institute of Science and Technology, Daejeon, South Korea;Department of Mathematics Education, Kyungpook National University, Daegu, Korea;Department of Mathematics, COMSATS Institute of Information Technology, Islamabad, Pakistan;Department of Mathematics, Lahore University of Management Sciences, Lahore, Pakistan

关键词: anomalous fluid;    Oldroyd-B fluid;    finite element method;    stability;    convergence;    35A15;    76A05;    76A10;    76D99;    76M10;   

DOI  :  10.1186/s13662-016-0961-9

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this article, we study an unsteady flow of an anomalous Oldroyd-B fluid confined between two infinite parallel plates subject to no-slip condition at boundary. The flow is induced by a linear acceleration of the lower plate in its own plane. A standard Galerkin finite element method is adopted to construct an approximate solution blended with a finite difference approximation for Caputo fractional time derivatives. The convergence of the proposed numerical scheme is substantiated, and error estimates are provided in appropriate norms. Some adequate numerical simulations are performed in order to elucidate the dominance of characteristic flow parameters of velocity field in the prescribed configuration.

【 授权许可】

CC BY