Space–time finite element method for the multi-term time–space fractional diffusion equation on a two-dimensional domain

2019 ◽  
Vol 78 (5) ◽  
pp. 1367-1379 ◽  
Author(s):  
Weiping Bu ◽  
Shi Shu ◽  
Xiaoqiang Yue ◽  
Aiguo Xiao ◽  
Wei Zeng
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Diffusion Equation ◽  
Fractional Diffusion ◽  
Space Time ◽  
Fractional Diffusion Equation ◽  
Two Dimensional ◽  
Time Space ◽  
Space Fractional Diffusion Equation ◽  
Dimensional Domain

A New Numerical Scheme for the Space Fractional Diffusion Equation

2014 ◽  
Vol 599-601 ◽  
pp. 1305-1308 ◽  
Author(s):  
Jun Ying Cao ◽  
Zi Qiang Wang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Difference ◽  
Diffusion Equation ◽  
Efficient Method ◽  
Numerical Scheme ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Numerical Examples ◽  
Space Fractional Diffusion Equation

We construct the numerical method of the space fractional diffusion equation in this paper. We propose an efficient method for its numerical solution. This method is based on a finite difference in time and finite element method in space. Convergence of the method is rigorously established. A series of numerical examples are provided to support the theoretical claims.

scholarly journals A Numerical Solution to Fractional Diffusion Equation for Force-Free Case

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
O. Tasbozan ◽  
A. Esen ◽  
N. M. Yagmurlu ◽  
Y. Ucar
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Diffusion Equation ◽  
Exact Analytical Solution ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Spline Functions ◽  
B Spline ◽  
Numerical Examples ◽  
Free Case

A collocation finite element method for solving fractional diffusion equation for force-free case is considered. In this paper, we develop an approximation method based on collocation finite elements by cubic B-spline functions to solve fractional diffusion equation for force-free case formulated with Riemann-Liouville operator. Some numerical examples of interest are provided to show the accuracy of the method. A comparison between exact analytical solution and a numerical one has been made.

scholarly journals Parameter Identification in the Two-Dimensional Riesz Space Fractional Diffusion Equation

2020 ◽  
Vol 4 (3) ◽  
pp. 39
Author(s):  
Rafał Brociek ◽  
Agata Chmielowska ◽  
Damian Słota
Keyword(s):  
Differential Equation ◽  
Diffusion Equation ◽  
Parameter Identification ◽  
Fractional Diffusion ◽  
Riesz Space ◽  
Fractional Diffusion Equation ◽  
Two Dimensional ◽  
Numerical Examples ◽  
Space Fractional Diffusion Equation ◽  
Swarm Intelligence Algorithm

This paper presents the application of the swarm intelligence algorithm for solving the inverse problem concerning the parameter identification. The paper examines the two-dimensional Riesz space fractional diffusion equation. Based on the values of the function (for the fixed points of the domain) which is the solution of the described differential equation, the order of the Riesz derivative and the diffusion coefficient are identified. The paper includes numerical examples illustrating the algorithm’s accuracy.

scholarly journals Identifying the space source term problem for time-space-fractional diffusion equation

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Erdal Karapinar ◽  
Devendra Kumar ◽  
Rathinasamy Sakthivel ◽  
Nguyen Hoang Luc ◽  
N. H. Can
Keyword(s):  
Diffusion Equation ◽  
Source Term ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Choice Rule ◽  
Parameter Choice ◽  
Time Space ◽  
Space Fractional Diffusion Equation ◽  
Ill Posed ◽  
Regularized Solution

Abstract In this paper, we consider an inverse source problem for the time-space-fractional diffusion equation. Here, in the sense of Hadamard, we prove that the problem is severely ill-posed. By applying the quasi-reversibility regularization method, we propose by this method to solve the problem (1.1). After that, we give an error estimate between the sought solution and regularized solution under a prior parameter choice rule and a posterior parameter choice rule, respectively. Finally, we present a numerical example to find that the proposed method works well.

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