Mimetic and pressure robust finite element methods for incompressible flows

Garth N. Wells, Department of Engineering, University of Cambridge

I will present some finite element methods for incompressible flows that preserve exactly some important physical features. A particular focus will be on methods for which error estimates for the velocity do not depend on the pressure field. Common elements, such at the Taylor-Hood pair, do not have this property. Having methods for which the velocity error does not depend on the pressure is particularly important in a range of problems where the pressure field may be difficult to capture well and may then have a particularly deleterious effect on the quantity of real interest, the velocity field. It is also critical for modelling buoyancy-driven flows. With a view to applications, I will also consider how these methods can be appropriately preconditioned to create fast and scalable solvers.