Faustmann, M., Stephan, E. P., & Wörgötter, D. (2023). Two-level error estimation for the integral fractional Laplacian. Computational Methods in Applied Mathematics, 23(3), 603–621. https://doi.org/10.1515/cmam-2022-0195
For the singular integral definition of the fractional Laplacian, we consider an adaptive finite element method steered by two-level error indicators. For this algorithm, we show linear convergence in two and three space dimensions as well as convergence of the algorithm with optimal algebraic rates in 2D, when newest vertex bisection is employed for mesh refinement. A key step hereby is an equivalence of the nodal and Scott-Zhang interpolation operators in certain weighted L²-norms.
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