Analytical solution and nonconforming finite element approximation for the 2D multi-term fractional subdiffusion equation

The current paper focuses on analytical solution and numerical approximation for the two-dimensional(2D) multi-term time fractional subdiffusion equation. In order to derive an effective numerical solution of the equation, an unconditionally stable fully-discrete approximate scheme is established by using a modified L1 approximation and spatial nonconforming finite element method, which has many advantages comparing with conforming one. Moreover, by employing the Crouzeix-Raviart type EQ1rot nonconforming element and dealing with fractional derivatives skillfully, temporal optimal order error estimates and spatial optimal convergence rates in both L2-norm and broken energy norm are proposed without restrictions between time step and mesh size. Then, several numerical results have been provided to give an insight into the efficiency and reliability of the theoretical analysis. Finally, the derivation process of the analytical solution is presented by means of a method of separating variables.