hp-FEM for the fractional heat equation

J Markus Melenk, A Rieder - IMA Journal of Numerical Analysis, 2021‏ - academic.oup.com
We consider a time-dependent problem generated by a nonlocal operator in space.
Applying for the spatial discretization a scheme based on-finite elements and a Caffarelli …

Stable decompositions of hp-BEM spaces and an optimal Schwarz preconditioner for the hypersingular integral operator in 3D

M Karkulik, JM Melenk, A Rieder - ESAIM: Mathematical Modelling …, 2020‏ - esaim-m2an.org
We consider fractional Sobolev spaces H θ (Γ), θ∈[0, 1] on a 2D surface Γ. We show that
functions in H θ (Γ) can be decomposed into contributions with local support in a stable way …