A Dimensional-Splitting Weak Galerkin Finite Element Method for 2D Time-Fractional Diffusion Equation

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 \(\beta \) $\beta$ , \(0<\beta <1\) $0<\beta <1$ 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 \(L^2\) $L^2$ -norm. Finally, we present a numerical experiment to demonstrate the suitability of the stated method.