On the Convergence in $H^1$-Norm for the Fractional Laplacian
On the Convergence in $H^1$-Norm for the Fractional Laplacian
We consider the numerical solution of the fractional Laplacian of index $s\in(1/2,1)$ in a bounded domain $\Omega$ with homogeneous boundary conditions. Its solution a priori belongs to the fractional-order Sobolev space ${\widetilde H}^s(\Omega)$. For the Dirichlet problem and under suitable assumptions on the data, it can be shown that its …