α#x02010;robust H1‐norm convergence analysis of L1FEM‐ADI scheme for 2D/3D subdiffusion equation with initial singularity

Abstract

For solving the two‐ and three‐dimensional time‐fractional subdiffusion equations (TFDE) whose solutions have weak singularities, the L1FEM‐ADI scheme is established. The Caputo time‐fractional derivative is discretized by L1 scheme on nonuniform mesh, and finite element method (FEM) is utilized in spatial direction. The high dimensional problem is transformed into one‐dimensional problems by alternating direction implicit (ADI) method. In order to avoid the error bound blowup phenomenon when the order of fractional derivative , an improved discrete fractional Grönwall inequality is employed. Stability and convergence of the fully discrete schemes in ‐norm sense are rigorously established, and the theoretical analysis is sharp as shown in numerical results.