Journal Article10.1016/J.MATCOM.2020.12.033
Two-grid methods for nonlinear time fractional diffusion equations by L1-Galerkin FEM
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TL;DR: In this article, two efficient two-grid algorithms with L 1 scheme are presented for solving two-dimensional nonlinear time fractional diffusion equations, where the Newton iteration approach and correction technique are applied to linearize the discrete equations.
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About: This article is published in Mathematics and Computers in Simulation. The article was published on 01 Jul 2021. The article focuses on the topics: Nonlinear system & Finite element method.
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Citations
A two-grid mixed finite volume element method for nonlinear time fractional reaction-diffusion equations
Zhichao Fang,Ruixia Du,Hong Li,Yang Liu +3 more
- 01 Jan 2022
TL;DR: In this paper, a two-grid mixed finite volume element (MFVE) algorithm is presented for the nonlinear time fractional reaction-diffusion equations, where the Caputo fractional derivative is approximated by the classical $ L 1 $-formula.
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Two-grid finite element methods for nonlinear time fractional variable coefficient diffusion equations
Yunhua Zeng,Zhijun Tan +1 more
TL;DR: In this article , an efficient two-grid finite element method was proposed for solving the nonlinear time fractional variable coefficient diffusion equations, in which the temporal direction was approximated by the L2−1σ scheme.
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A two-grid mixed finite volume element method for nonlinear time fractional reaction-diffusion equations
01 Jan 2022
TL;DR: In this paper , a two-grid mixed finite volume element (MFVE) algorithm is presented for the nonlinear time fractional reaction-diffusion equations, where the Caputo fractional derivative is approximated by the classical $ L 1 $-formula.
6
A fourth order accurate numerical method for non-linear time fractional reaction diffusion equation on a bounded domain
TL;DR: In this article , a high-order numerical scheme is proposed and analyzed to solve the non-linear time fractional reaction-diffusion equation (RDE) of order α∈(0,1).
5
References
•Book
The Finite Element Method for Elliptic Problems
Philippe G. Ciarlet,J. T. Oden +1 more
- 01 Jan 1978
TL;DR: The finite element method has been applied to a variety of nonlinear problems, e.g., Elliptic boundary value problems as discussed by the authors, plate problems, and second-order problems.
8.9K
•Book
Applications Of Fractional Calculus In Physics
Rudolf Hilfer
- 02 Mar 2000
TL;DR: An introduction to fractional calculus can be found in this paper, where Butzer et al. present a discussion of fractional fractional derivatives, derivatives and fractal time series.
6.5K