• Victor Calo, Curtin University
• Santiago Badia, Monash University
• Jerome Droniou, Monash University

This minisymposium will discuss novel techniques for the numerical approximation of partial differential equations, such as unfitted finite element methods, mimetic discretisations, virtual element methods, finite element exterior calculus, hybrid discontinuous Galerkin and high order methods, discontinuous Petrov-Galerkin methods, numerical neural networks, structure-preserving, and monotonic finite elements. Such schemes provide desired properties like greater flexibility in the geometrical discretisation step, improved approximability properties, and enhanced stability. These technologies offer many opportunities in computational mechanics as well as new mathematical challenges. Contributions to this minisymposium can address new method development, mathematical analysis, and their application to engineering science problems that benefit from these novel techniques, such as flow simulations, material design and microstructural discretisation, topology optimisation and additive manufacturing, deformation of nonlinear continua, fracture modelling, and computer graphics and animations.