A Petrov-Galerkin finite element method for variable-coefficient fractional diffusion equations

We utilize the discontinuous Petrov-Galerkin (DPG) framework to develop a Petrov-Galerkin finite element method for variable-coefficient fractional diffusion equations. We prove the well-posedness and optimal-order convergence of the Petrov-Galerkin finite element method. Numerical examples are presented to verify the theoretical results.