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Two efficient Galerkin finite element methods for the modified anomalous subdiffusion equation

ABSTRACT In this paper, we consider the numerical approximation of the modified anomalous subdiffusion model which involves the Riemann–Liouville derivatives in time. We propose two robust fully discrete finite element methods by employing the piecewise linear Galerkin finite element method in space and the convolution quadrature in time generated by the backward Euler and the second-order backward difference methods. The error estimates for semidiscrete and fully discrete schemes are investigated with respect to the data regularity. Furthermore, we numerically compare our numerical schemes with a Crank–Nicolson finite element method to illustrate the efficiency of our methods and confirm the theoretical results.