Numerical algorithm based on an implicit fully discrete local discontinuous Galerkin method for the fractional diffusion-wave equation (Q478200)

The numerical approximation of a fractional diffusion wave-equation is studied. The authors develop a fully discrete local discontinuous Galerkin finite element method for solving a class of fractional diffusion-wave equations (cf. [\textit{R. Du} et al., Appl. Math. Modelling 34, No. 10, 2998--3007 (2010; Zbl 1201.65154)]). It is proved that the scheme is unconditionally stable. A certain \(L_2\) error convergence rate is obtained. Numerical examples to support the accuracy and capability of the method are also given.