Local discontinuous Galerkin method for the fractional diffusion equation with integral fractional Laplacian

Abstract

In this paper, we provide a framework of designing the local discontinuous Galerkin scheme for integral fractional Laplacian (−∆) s with s ∈ (0, 1) in two dimensions. We theoretically prove and numerically verify the numerical stability and convergence of the scheme with the convergence rate no worse than O(h k+ 1 2 ).