Analysis of Schrodinger operators with inverse square potentials II: FEM and approximation of eigenfunctions in the periodic case
journal contributionposted on 01.04.2015, 10:58 by Eugenie HunsickerEugenie Hunsicker, Hengguang Li, Victor Nistor, Ville Uski
In this article, we consider the problem of optimal approximation of eigenfunctions of Schrödinger operators with isolated inverse square potentials and of solutions to equations involving such operators. It is known in this situation that the finite element method performs poorly with standard meshes. We construct an alter- native class of graded meshes, and prove and numerically test optimal approximation results for the finite element method using these meshes. Our numerical tests are in good agreement with our theoretical results.
Contract grant sponsor: Leverhulme Trust (E.H.); contract grant number: J11695 Contract grant sponsor: NSF (H.L.); contract grant number: 1158839 Contract grant sponsor: NSF (V.N.); contract grant numbers: OCI-0749202 and DMS-1016556
- Mathematical Sciences