Numerical approximations of a norm-preserving gradient flow and applications to an optimal partition problem**This paper is published as part of a collection in honour of Todd Dupont's 65th birthday.

Abstract

We present and analyse numerical approximations of a norm-preserving gradient flow and consider applications to an optimal eigenvalue partition problem. We consider various discretizations and demonstrate that many of the properties shared by the continuous counterpart can be preserved at the discrete level. The numerical algorithms are then used to study the nonlinear and non-local interfacial dynamics associated with the optimal partition.