Sharp error estimates of a spectral Galerkin method for a diffusion-reaction equation with integral fractional Laplacian on a disk

We investigate a spectral Galerkin method for the two-dimensional fractional diffusion-reaction equations on a disk. We first prove regularity estimates of solutions in the weighted Sobolev space. Then we obtain optimal convergence orders of a spectral Galerkin method for the fractional diffusion-reaction equations in the L 2 L^2 and energy norm. We present numerical results to verify the theoretical analysis.