Nonconforming Mixed FEM Analysis for Multi-Term Time-Fractional Mixed Sub-Diffusion and Diffusion-Wave Equation with Time-Space Coupled Derivative

The main contents of this paper are to establish a finite element fully-discrete approximate scheme for multi-term time-fractional mixed sub-diffusion and diffusion -wave equation with spatial variable coefficient, which contains a time-space coupled derivative. The nonconforming EQrot 1 element and Raviart-Thomas element are em-ployed for spatial discretization, and L1 time-stepping method combined with the Crank-Nicolson scheme are applied for temporal discretization. Firstly, based on some significant lemmas, the unconditional stability analysis of the fully-discrete scheme is acquired. With the assistance of the interpolation operator Ih and projection opera-tor Rh, superclose and convergence results of the variable u in H1-norm and the flux p similar to= kappa 5(x) backward difference u(x,t) in L2-norm are obtained, respectively. Furthermore, the global su-perconvergence results are derived by applying the interpolation postprocessing tech-nique. Finally, the availability and accuracy of the theoretical analysis are corroborated by experimental results of numerical examples on anisotropic meshes.