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