High Spatial Accuracy Analysis of Linear Triangular Finite Element for Distributed Order Diffusion Equations

Abstract

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.