Contributions to Books:

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.

English abstract:
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

Electronic version of the publication:

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