Research

My research interests comprise:

• High-order methods: finite element, discontinuous Galerkin, hybridisable discontinuous Galerkin

• Low-order methods: finite volume, face-centred finite volume

• Error & adaptivity: a posteriori estimates, goal-oriented estimates, mesh adaptation, anisotropic meshes, degree adaptation

• Dimensionality & complexity reduction: scientific machine learning, reduced order models, proper generalised decomposition, proper orthogonal decomposition, data augmentation, multi-fidelity, domain decomposition

• PDE-constrained optimisation: shape optimisation, topology optimisation, multiobjective optimisation, moving interfaces

• Development of open-source CSE software

• Applications: computational fluid dynamics, computational solid mechanics, multiphysics, image segmentation, industrial problems, sustainability