In this talk, we discuss a quadrature error analysis of -FEM for the one-dimensional integral fractional Laplacian. In practice, it is not possible to set up the linear system of equations for the hp-FEM exactly due to the presence of the kernel function of the integral fractional Laplacian. Therefore, a computable numerical approximation for the -FEM solution with quadrature-techniques does not need to have the same convergence rate. We show for our hp-FEM implementation that taking a number of quadrature points slightly exceeding the polynomial degree is enough to preserve root exponential convergence.
This event takes place in hybrid form (in person and online on Zoom). Slides and additional materials are available on the Moodle service of the University of Vienna. If you want to participate, please write an email to matteo.tommasini@univie.ac.at.