The time discontinuous space-time finite element method for fractional diffusion-wave equation

2020 ◽  
Vol 150 ◽  
pp. 105-116 ◽  
Author(s):  
Yunying Zheng ◽  
Zhengang Zhao
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Wave Equation ◽  
Fractional Diffusion ◽  
Space Time ◽  
Diffusion Wave ◽  
Element Method

scholarly journals Error estimates for a robust finite element method of two-term time-fractional diffusion-wave equation with nonsmooth data

2021 ◽  
Author(s):  
Lijuan Nong ◽  
An Chen ◽  
Jianxiong Cao
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Wave Equation ◽  
Error Estimates ◽  
Piecewise Linear ◽  
Fractional Diffusion ◽  
Diffusion Wave ◽  
Nonsmooth Data ◽  
Fully Discrete ◽  
Element Method

In this paper, we consider a two-term time-fractional diffusion-wave equation which involves the fractional orders $\alpha\in (1, 2)$ and $\beta\in(0, 1)$, respectively. By using piecewise linear Galerkin finite element method in space and convolution quadrature based on second-order backward difference method in time, we obtain a robust fully discrete scheme. Error estimates for semidiscrete and fully discrete schemes are established with respect to nonsmooth data. Numerical experiments for two-dimensional problems are provided to illustrate the efficiency of the method and conform the theoretical results.

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.

scholarly journals High-accuracy analysis of finite-element method for two-term mixed time-fractional diffusion-wave equations

2018 ◽  
Vol 48 (7) ◽  
pp. 871-887 ◽  
Author(s):  
Yabing WEI ◽  
Yanmin ZHAO ◽  
Yifa TANG ◽  
Fenling WANG ◽  
Zhengguang SHI ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Wave Equations ◽  
Fractional Diffusion ◽  
High Accuracy ◽  
Accuracy Analysis ◽  
Diffusion Wave ◽  
Element Method
Sign in / Sign up

Export Citation Format

Share Document