A Petrov-Galerkin finite element method using polyfractonomials to solve stochastic fractional differential equations

2021 ◽  
Author(s):  
Nazanin Abedini ◽  
Ali Foroush Bastani ◽  
Bijan Zohouri Zangeneh
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Galerkin Finite Element Method ◽  
Galerkin Finite Element ◽  
Fractional Differential ◽  
Stochastic Fractional Differential Equations ◽  
Element Method

Application of low-dimensional finite element method to fractional diffusion equation

2014 ◽  
Vol 05 (04) ◽  
pp. 1450022 ◽  
Author(s):  
Jincun Liu ◽  
Hong Li ◽  
Zhichao Fang ◽  
Yang Liu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Differential Equations ◽  
Diffusion Equation ◽  
Fractional Differential Equations ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Fractional Differential ◽  
Low Dimensional ◽  
Element Method

Classical finite element method (FEM) has been applied to solve some fractional differential equations, but its scheme has too many degrees of freedom. In this paper, a low-dimensional FEM, whose number of basis functions is reduced by the theory of proper orthogonal decomposition (POD) technique, is proposed for the time fractional diffusion equation in two-dimensional space. The presented method has the properties of low dimensions and high accuracy so that the amount of computation is decreased and the calculation time is saved. Moreover, error estimation of the method is obtained. Numerical example is given to illustrate the feasibility and validity of the low-dimensional FEM in comparison with traditional FEM for the time fractional differential equations.

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