scholarly journals The Unstructured Mesh Finite Element Method for the Two-Dimensional Multi-term Time–Space Fractional Diffusion-Wave Equation on an Irregular Convex Domain

2018 ◽  
Vol 77 (1) ◽  
pp. 27-52 ◽  
Author(s):  
Wenping Fan ◽  
Xiaoyun Jiang ◽  
Fawang Liu ◽  
Vo Anh
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Wave Equation ◽  
Convex Domain ◽  
Unstructured Mesh ◽  
Fractional Diffusion ◽  
Two Dimensional ◽  
Diffusion Wave ◽  
Time Space ◽  
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.

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