Symmetric stabilized FEM for time-fractional convection–diffusion–reaction equations

This paper presents a stabilized finite element method for solving time-fractional convection–diffusion-reaction equations. The approach combines a symmetric stabilization technique in space with a time-stepping method based on a convolution quadrature generated by the backward method and an L1 finite difference scheme. The stability of the semi-discrete problem is analyzed, and optimal error estimates are initially derived under high regularity assumptions on the initial condition and the solution. To relax these regularity requirements, a refined energy technique is employed, extending the error analysis to nonsmooth initial conditions and increasing the method’s applicability. Numerical simulations are presented, confirming the effectiveness and accuracy of the proposed scheme.