The research, implementation and application of high-order and high-fidelity methods is one of the main research projects at SherwinLab. We mainly focus on the Spectral/hp element method and high-order mesh generation, focusing on the software package Nektar++.

Nektar++ is a tensor product based finite element package designed to allow one to construct efficient classical low polynomial order h-type solvers (where h is the size of the finite element) as well as higher p-order piecewise polynomial order solvers.

We highlight the main research areas in this topic as:

  • Mesh generation for high order compact approximations

  • High order particle tracking

  • Efficiency of high and low order discretisations

  • Elliptic preconditioning of unstructured hybrid spectral/hp element methods

  • Ficitious domain methods for high order discretisations