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The Efficient Finite Element Methods for Time-Fractional Oldroyd-B Fluid Model Involving Two Caputo Derivatives

An Chen*
College of Science, Guilin University of Technology, Guilin, 541004, China
* Corresponding Author: An Chen. Email:

Computer Modeling in Engineering & Sciences 2020, 125(1), 173-195. https://doi.org/10.32604/cmes.2020.011871

Received 02 June 2020; Accepted 10 August 2020; Issue published 18 September 2020

Abstract

In this paper, we consider the numerical schemes for a timefractional Oldroyd-B fluid model involving the Caputo derivative. We propose two efficient finite element methods by applying the convolution quadrature in time generated by the backward Euler and the second-order backward difference methods. Error estimates in terms of data regularity are established for both the semidiscrete and fully discrete schemes. Numerical examples for two-dimensional problems further confirm the robustness of the schemes with first- and second-order accurate in time.

Keywords

Oldroyd-B fluid model; caputo derivative; finite element method; convolution quadrature; error estimate; data regularity

Cite This Article

Chen, A. (2020). The Efficient Finite Element Methods for Time-Fractional Oldroyd-B Fluid Model Involving Two Caputo Derivatives. CMES-Computer Modeling in Engineering & Sciences, 125(1), 173–195.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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