Galerkin finite element method for two-dimensional Riesz space fractional diffusion equations

2014 ◽  
Vol 276 ◽  
pp. 26-38 ◽  
Author(s):  
Weiping Bu ◽  
Yifa Tang ◽  
Jiye Yang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Fractional Diffusion ◽  
Riesz Space ◽  
Diffusion Equations ◽  
Two Dimensional ◽  
Galerkin Finite Element Method ◽  
Galerkin Finite Element ◽  
Fractional Diffusion Equations ◽  
Element Method

scholarly journals A GALERKIN FINITE ELEMENT METHOD TO SOLVE FRACTIONAL DIFFUSION AND FRACTIONAL DIFFUSION-WAVE EQUATIONS

2013 ◽  
Vol 18 (2) ◽  
pp. 260-273 ◽  
Author(s):  
Alaattin Esen ◽  
Yusuf Ucar ◽  
Nuri Yagmurlu ◽  
Orkun Tasbozan
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Wave Equations ◽  
Numerical Solutions ◽  
Fractional Diffusion ◽  
Galerkin Finite Element Method ◽  
Diffusion Wave ◽  
Galerkin Finite Element ◽  
Base Functions ◽  
Element Method

In the present study, numerical solutions of the fractional diffusion and fractional diffusion-wave equations where fractional derivatives are considered in the Caputo sense have been obtained by a Galerkin finite element method using quadratic B-spline base functions. For the fractional diffusion equation, the L1 discretizaton formula is applied, whereas the L2 discretizaton formula is applied for the fractional diffusion-wave equation. The error norms L 2 and L ∞ are computed to test the accuracy of the proposed method. It is shown that the present scheme is unconditionally stable by applying a stability analysis to the approximation obtained by the proposed scheme.

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