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A dimensional-splitting weak galerkin finite element method for 2D time-fractional diffusion equation
(Springer, 2024) Seal, Aniruddha; Natesan, Srinivasan; Toprakseven, Şuayip
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, 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-norm. Finally, we present a numerical experiment to demonstrate the suitability of the stated method.