A Dimensional-Splitting Weak Galerkin Finite Element Method for 2D Time-Fractional Diffusion Equation
Journal of Scientific Computing, vol.98, no.3, 2024 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 98 Issue: 3
- Publication Date: 2024
- Doi Number: 10.1007/s10915-023-02448-3
- Journal Name: Journal of Scientific Computing
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Keywords: ADI method, Error analysis, Numerical experiments, Operator-splitting method, Stability, Time-fractional diffusion, Weak Galerkin finite element method
- Yozgat Bozok University Affiliated: Yes
Abstract
In this article, the weak Galerkin finite element method, coupled with an operator-splitting method or known as dimensional-splitting technique, is proposed to solve a class of 2D time-fractional diffusion equation of order β , 0 < β< 1 numerically. The time-fractional term is discretized using the well-known non-uniform L1-method, as the integer-order temporal derivatives of the solution blow up at the initial point. For the spatial discretization, a dimensional-splitting weak Galerkin finite element method is used in both x and y directions over a uniform mesh. The stability and the optimal error estimate of the proposed scheme are addressed in the L2 -norm. Finally, we present a numerical experiment to demonstrate the suitability of the stated method.