I will present some recent finite element methods that have attractive mimetic properties for incompressible flows. A particular feature is "pressure robustness" for mixed methods for incompressible flows, where a priori error estimates for the velocity are independent of the pressure approximation. With a view to extreme scale computing, the generalisation of the methods to high-order geometries and various cell types will be discussed, and provably optimal preconditioning strategies for the methods presented.
Garth Wells is the Hibbitt Professor of Solid Mechanics at the Department of Engineering at University of Cambridge and a Fellow of Jesus College. Prior to his arrival at Cambridge he held an academic post at Delft University of Technology and research fellowships at University of Texas Austin and Stanford University. He received his PhD from Delft University of Technology and undergraduate degree from The University of Western Australia. He has been a leader of the FEniCS Project since 2005 and a strong advocate for the community development of open-source scientific software.