L. Banjai, J. Melenk, C. Schwab:

"Exponential Convergence of hp FEM for Spectral Fractional Diﬀusion in Polygons";

in: "ASC Report 30/2020", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2020, ISBN: 978-3-902627-13-1, 1 - 37.

For the spectral fractional diﬀusion operator of order 2s ∈ (0, 2)

in bounded, curvilinear polygonal domains Ω ⊂ R2 we prove exponential con-vergence of two classes of hp discretizations under the assumption of analytic data (coeﬃcients and source terms, without any boundary compatibility), in the natural fractional Sobolev norm Hs(Ω). The ﬁrst hp discretization is based on writing the solution as a co-normal derivative of a 2 + 1-dimensional local, linear elliptic boundary value problem, to which an hp-FE discretization is applied. A diagonalization in the extended variable reduces the numerical ap-proximation of the inverse of the spectral fractional diﬀusion operator to the numerical approximation of a system of local, decoupled, second order reaction-diﬀusion equations in Ω.

ionalFractional diﬀusion · nonlocal operators · Dunford-Taylor calculus · anisotropic hp-reﬁnement · geometric corner reﬁnement

http://www.asc.tuwien.ac.at/preprint/2020/asc30x2020.pdf

Created from the Publication Database of the Vienna University of Technology.