ADI Finite Element Galerkin Methods for Two-dimensional Tempered Fractional Integro-differential Equations

Three alternating direction implicit (ADI) finite element Galerkin methods for solving two-dimensional tempered fractional integro-differential equations are formulated and analyzed. For the time discretization, these methods are based on the backward Euler scheme, the Crank–Nicolson scheme and the second-order backward differentiation formula, respectively, each combined with an appropriate convolution quadrature rule. For each technique, optimal error estimates are derived and validated by numerical experiments.