| Abstract: |
| In this talk we consider the integral fractional Laplace equation on bounded domains. We first review the basic theories including the regularity of solutions and convergence rates of standard conforming finite element method. Next, we introduce a ``DG`` formulation motivated by an integration by parts formula for fractional Laplacian and establish the well-posedness of this discretization. We also derive the convergence rates and justify its optimality by some numerical experiments. Some variants of the bilinear form and hanging nodes on the shape-regular mesh are also permitted in our theory. In the end, we apply this idea to the problem of fractional Laplacian with order higher than one. |
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