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

01/20/2021

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by   Daxin Nie, et al.

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In this paper, we provide a framework of designing the local discontinuous Galerkin scheme for integral fractional Laplacian (-Δ)^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).