Local Convergence of the FEM for the Integral Fractional Laplacian
Markus Faustmann, Michael Karkulik, Jens Markus Melenk · SIAM Journal on Numerical Analysis · 2022
For first-order discretizations of the integral fractional Laplacian, we provide sharp local error estimates on proper subdomains in both the local $H^1$-norm and the localized energy norm. Our estimates have the form of a local best approximation error plus a global error measured in a weaker norm.