Optimal adaptivity and preconditioning for the fractional Laplacian
M Faustmann, JM Melenk, M Parvizi… - Proceedings of …, 2019 - ci2ma.udec.cl
We present novel inverse estimates for the (integral) fractional Laplacian. More precisely, we
show that a weighted L2-norm, where the weight is a power of the local mesh-width, of the
fractional Laplacian can be bounded by the energy norm. Generalizing the arguments used
in the boundary element method,[1], the non-local operator is split into a localized near-field
and a smoother far-field part, which is treated using the so-called Caffarelli-Silvestre
extension problem and interior regularity estimates. Weighted L2-norms appear naturally in …
show that a weighted L2-norm, where the weight is a power of the local mesh-width, of the
fractional Laplacian can be bounded by the energy norm. Generalizing the arguments used
in the boundary element method,[1], the non-local operator is split into a localized near-field
and a smoother far-field part, which is treated using the so-called Caffarelli-Silvestre
extension problem and interior regularity estimates. Weighted L2-norms appear naturally in …
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