In this paper, an effective numerical fully discrete finite element scheme for the distributed order time fractional diffusion equations is developed. By use of the composite trapezoid formula and the well-known $L1$ formula approximation to the distributed order derivative and linear triangular finite element approach for the spatial discretization, we construct a fully discrete finite element scheme. Based on the superclose estimate between the interpolation operator and the Ritz projection operator and the interpolation post-processing technique, the superclose approximation of the finite element numerical solution and the global superconvergence are proved rigorously, respectively. Finally, a numerical example is presented to support the theoretical results.
"High Spatial Accuracy Analysis of Linear Triangular Finite Element for Distributed Order Diffusion Equations." Taiwanese J. Math. 24 (3) 695 - 708, June, 2020. https://doi.org/10.11650/tjm/190803