Nonconforming quasi-Wilson finite element method for 2D multi-term time fractional diffusion-wave equation on regular and anisotropic meshes

摘要

The paper mainly focuses on studying nonconforming quasi-Wilson finite element fully-discrete approximation for two dimensional (2D) multi-term time fractional diffusion-wave equation (TFDWE) on regular and anisotropic meshes. Firstly, based on the Crank–Nicolson scheme in conjunction with L1-approximation of the time Caputo derivative of order α ∈ (1, 2), a fully-discrete scheme for 2D multi-term TFDWE is established. And then, the approximation scheme is rigorously proved to be unconditionally stable via processing fractional derivative skillfully. Moreover, the superclose result in broken H1-norm is deduced by utilizing special properties of quasi-Wilson element. In the meantime, the global superconvergence in broken H1-norm is derived by means of interpolation postprocessing technique. Finally, some numerical results illustrate the correctness of theoretical analysis on both regular and anisotropic meshes.