A Dimensionally Reduced Weak Galerkin FEM for Solving 2D Multi‐Term Time‐Fractional Diffusion Equation

ABSTRACT This article presents a weak Galerkin finite element method combined with a dimensional‐reduction strategy to numerically address a class of two‐dimensional multi‐term time‐fractional diffusion equations. The temporal fractional derivative is discretized using the widely recognized non‐uniform scheme, which is particularly effective in managing the singular behavior of integer‐order temporal derivatives of the solution near the initial time. To handle spatial discretization, we adopt the dimensionally reduced weak Galerkin finite element method. This technique solves the problem sequentially along both spatial axes using a uniform mesh. The stability analysis is presented, and the optimal error estimates are derived in the norm. Lastly, numerical experiments are performed to confirm the theoretical findings and illustrate the effectiveness of the suggested approach.