Stability and convergence of a fully discrete local discontinuous Galerkin method for multi-term time fractional diffusion equations (Q1681775)

The author develops a fully discrete local discontinuous Galerkin method for a class of multi-term time fractional diffusion equations. The approach combines a local discontinuous Galerkin method in spatial direction with classical \(L^1\) approximation in temporal direction. It is obtained that the method is unconditionally stable and convergent with order \(O(h^{k+1} + (\Delta t)^{2-\alpha})\), where \(k\), \(h\), and \(t\) are the degree of piecewise polynomial, the space, and time step sizes, respectively. Numerical experiments are also presented in order to support the theoretical findings.