Finite element modelling/method (FEM) is indispensable for the accurate and rigorous numerical solution of continuum models arising in Engineering, Physics, Biology and other disciplines. Despite FEM’s astounding success, large classes of evolution PDE problems remain very expensive or even intractable computationally.

The proposed research aims to address this computational challenge with the development of a new paradigm of reduced-complexity FEM, using novel mesh-order (hp-version), space-time, adaptive, discontinuous Galerkin (dG) methods on meshes consisting of, possibly anisotropic, polygonal/polyhedral element shapes.