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 $(-\Delta {)}^s$ with $s\in (0,1)$ in two dimensions. We theoretically prove and numerically verify the numerical stability and convergence of the scheme with the convergence rate no worse than $\mathcal{O}(h^{k+\frac{1}{2}})$.

11 pages