Markus Faustmann, Ernst P. Stephan, David Wörgötter
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Two-Level Error Estimation for the Integral Fractional Laplacian
Abstract 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 L^{2} -norms.
期刊介绍:
The highly selective international mathematical journal Computational Methods in Applied Mathematics (CMAM) considers original mathematical contributions to computational methods and numerical analysis with applications mainly related to PDEs.
CMAM seeks to be interdisciplinary while retaining the common thread of numerical analysis, it is intended to be readily readable and meant for a wide circle of researchers in applied mathematics.
The journal is published by De Gruyter on behalf of the Institute of Mathematics of the National Academy of Science of Belarus.