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

Published 20 Jan 2021 in math.NA and cs.NA | (2101.08260v1)

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 $\mathcal{O}(h^{{k+\frac{1}{2}})$.}