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ARTICLE

# Quadratic Finite Volume Element Schemes over Triangular Meshes for a Nonlinear Time-Fractional Rayleigh-Stokes Problem

Yanlong Zhang1, Yanhui Zhou2, Jiming Wu3,*

1 Graduate School of China Academy of Engineering Physics, Beijing, 100088, China
2 School of Data and Computer Science, Sun Yat-Sen University, Guangzhou, 510275, China
3 Institute of Applied Physics and Computational Mathematics, Beijing, 100088, China

* Corresponding Author: Jiming Wu. Email: Computer Modeling in Engineering & Sciences 2021, 127(2), 487-514. https://doi.org/10.32604/cmes.2021.014950

## Abstract

In this article, we study a 2D nonlinear time-fractional Rayleigh-Stokes problem, which has an anomalous sub-diffusion term, on triangular meshes by quadratic finite volume element schemes. Time-fractional derivative, defined by Caputo fractional derivative, is discretized through formula, and a two step scheme is used to approximate the time first-order derivative at time , where the nonlinear term is approximated by using a matching linearized difference scheme. A family of quadratic finite volume element schemes with two parameters are proposed for the spatial discretization, where the range of values for two parameters are , . For testing the precision of numerical algorithms, we calculate some numerical examples which have known exact solution or unknown exact solution by several kinds of quadratic finite volume element schemes, and contrast with the results of an existing quadratic finite element scheme by drawing diversified comparison plots and showing the detailed data of L2 error results and convergence orders. Numerical results indicate that, L2 error estimate of one scheme with parameters , is , and L2 error estimates of other schemes are , where h and denote the spatial and temporal discretization parameters, respectively.

## Keywords

Zhang, Y., Zhou, Y., Wu, J. (2021). Quadratic Finite Volume Element Schemes over Triangular Meshes for a Nonlinear Time-Fractional Rayleigh-Stokes Problem. CMES-Computer Modeling in Engineering & Sciences, 127(2), 487–514. 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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