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research-article

Galerkin finite element method for two-dimensional space and time fractional BlochTorrey equation

Authors:

Yifa TangAuthors Info & Claims

Journal of Computational Physics, Volume 350, Issue C

Pages 117 - 135

https://doi.org/10.1016/j.jcp.2017.08.051

Published: 01 December 2017 Publication History

Abstract

In this paper, we consider the Galerkin finite element method for the two-dimensional space and time fractional BlochTorrey equation (2D-STFBTE). Utilizing the L21 formula to discretize temporal Caputo derivative, we obtain the local truncation error with O(3) in the temporal direction, where is the order of time fractional derivative. Furthermore, the semi-discrete form for the problem is given and, the stability and convergence of the semi-discrete variational formulation are rigorously proved in L2 norm and fractional norm respectively. Then, we derive a fully discrete scheme for the 2D-STFBTE and investigate its convergence theoretically. Finally, extensive numerical results based on linear piecewise polynomials verify the theoretical results and show the effectiveness of the proposed scheme. Galerkin finite element method for the two-dimensional space and time fractional BlochTorrey equation is proposed.L21 fractional numerical differentiation formula is used to approximate the Caputo fractional derivative in time.Using the L21 formula, a semi-discrete variational formulation is obtained, and the stability and convergence of this scheme are investigated.Convergence of the fully discrete scheme is investigated.Some numerical examples based on linear piecewise polynomials are given to prove the correctness of the theoretical analysis.

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Cited By

Chen MLuan SLian Y(2021)Fractional SUPG finite element formulation for multi-dimensional fractional advection diffusion equationsComputational Mechanics10.1007/s00466-020-01951-w67:2(601-617)Online publication date: 1-Feb-2021
https://dl.acm.org/doi/10.1007/s00466-020-01951-w
Lin ZWang DQi DDeng L(2020)A Petrov–Galerkin finite element-meshfree formulation for multi-dimensional fractional diffusion equationsComputational Mechanics10.1007/s00466-020-01853-x66:2(323-350)Online publication date: 16-May-2020
https://dl.acm.org/doi/10.1007/s00466-020-01853-x
Bu WXiao A(2019)An h-p version of the continuous Petrov-Galerkin finite element method for Riemann-Liouville fractional differential equation with novel test basis functionsNumerical Algorithms10.1007/s11075-018-0559-281:2(529-545)Online publication date: 1-Jun-2019
https://dl.acm.org/doi/10.1007/s11075-018-0559-2

Galerkin finite element method for two-dimensional space and time fractional BlochTorrey equation
1. Mathematics of computing
  1. Mathematical analysis
    1. Differential equations
    2. Numerical analysis
2. Theory of computation

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Published In

cover image Journal of Computational Physics

Journal of Computational Physics Volume 350, Issue C

December 2017

504 pages

ISSN:0021-9991

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Copyright © Elsevier Inc.

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Academic Press Professional, Inc.

United States

Publication History

Published: 01 December 2017

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Cited By

Chen MLuan SLian Y(2021)Fractional SUPG finite element formulation for multi-dimensional fractional advection diffusion equationsComputational Mechanics10.1007/s00466-020-01951-w67:2(601-617)Online publication date: 1-Feb-2021
https://dl.acm.org/doi/10.1007/s00466-020-01951-w
Lin ZWang DQi DDeng L(2020)A Petrov–Galerkin finite element-meshfree formulation for multi-dimensional fractional diffusion equationsComputational Mechanics10.1007/s00466-020-01853-x66:2(323-350)Online publication date: 16-May-2020
https://dl.acm.org/doi/10.1007/s00466-020-01853-x
Bu WXiao A(2019)An h-p version of the continuous Petrov-Galerkin finite element method for Riemann-Liouville fractional differential equation with novel test basis functionsNumerical Algorithms10.1007/s11075-018-0559-281:2(529-545)Online publication date: 1-Jun-2019
https://dl.acm.org/doi/10.1007/s11075-018-0559-2

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