Finite Element Analysis of Nonlinear 2D Space-Time-Fractional Diffusion Equations Using the L2-1_σ Discretization Scheme

This study proposes a high-precision finite element method (FEM) for nonlinear two-dimensional space-time-fractional diffusion equations, combining the Galerkin spatial discretization with the L2- 1_σ temporal scheme. By rigorously analyzing unconditional stability and deriving error estimates, the method achieves spatial convergence of order 2 and temporal convergence of order 3-α , where α∈ (0,1) , validated through numerical experiments under diverse initial conditions. Compared to existing works focusing on linear systems or single-term fractional dynamics, this research innovatively extends the L2- 1_σ scheme to complex nonlinear space-time-coupled problems, demonstrating its capability to simultaneously handle nonlinearities and fractional derivatives while maintaining computational efficiency and geometric adaptability.