Faustmann, M., Karkulik, M., & Melenk, J. M. (2022). Local Convergence of the FEM for the Integral Fractional Laplacian. SIAM Journal on Numerical Analysis, 60(3), 1055–1082. https://doi.org/10.1137/20M1343853
finite element method; fractional Laplacian; local estimates; applied mathematics; computational mathematics; numerical analysis
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Abstract:
For first-order discretizations of the integral fractional Laplacian, we provide sharp local error estimates on proper subdomains in both the local 𝐻¹-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.
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Projekttitel:
Numerische Methoden Höherer Ordnung für nichtlokale Operatoren: F 6507-N36 (Fonds zur Förderung der wissenschaftlichen Forschung (FWF))
