Analysis of mixed finite element method (MFEM) for solving the generalized fractional reaction-diffusion equation on nonrectangular domains

In the current manuscript, we consider a generalized fractional reaction-diffusion equation. The considered model is based on the time fractional derivative. The developed scheme is based on two procedures. At first, we obtain a semi-discrete scheme for the temporal direction. The time fractional derivative is discretized by using a difference scheme with second-order accuracy. Thus, the final time-discrete formula has second order accuracy in the temporal direction. Then, we obtain a fully discrete scheme by applying the mixed finite element method (MFEM). For the constructed numerical technique, we prove the unconditional stability and also obtain an error bound for the full-discrete scheme by using the energy method. We employ some test problems to show the accuracy of the proposed technique. (C) 2019 Elsevier Ltd. All rights reserved.