${\mathscr{H}}$-matrix approximability of inverses of discretizations of the fractional Laplacian

• DOI: 10.1007/s10444-019-09718-5
• Publication Date: 2019-11-12T21:02:48Z
• Authors: Michael Karkulik; Jens Markus Melenk
• Keywords: FOS: Mathematics; Mathematics - Numerical Analysis; Numerical Analysis (math.NA); 0101 mathematics; 01 natural sciences

The integral version of the fractional Laplacian on a bounded domain is discretized by a Galerkin approximation based on piecewise linear functions on a quasi-uniform mesh. We show that the inverse of the associated stiffness matrix can be approximated by blockwise low-rank matrices at an exponential rate in the block rank.