The accuracy of an HDG method for conservative fractional diffusion equations

In this paper, we introduce and investigate the performance of a hybridizable discontinuous Galerkin (HDG) method for approximating the solution of conservative fractional diffusion equations (CFDE). The main attractive feature of these methods is the fact that the only globally coupled unknowns are those at the element boundaries. We first introduce the HDG method for the CFDE and prove the existence and uniqueness of the numerical solution provided that the stabilization parameter is strictly positive. We provide extensive numerical results to test the convergence behavior of the HDG approximation.