Space-time Taylor-Hood elements for incompressible flows

Space-time Taylor-Hood elements for incompressible flows

Douglas R. Q. Pacheco, Olaf Steinbach

Institute of Applied Mathematics, Graz University of Technology, Graz, Austria.
Graz Center of Computational Engineering, Graz University of Technology, Graz, Austria.



Space-time variational methods differ from time-stepping schemes by discretising the whole space-time domain with finite elements. This offers a natural framework for flow problems in moving domains and allows simultaneous parallelisation and adaptivity in space and time. For incompressible flows, the usual approach is to employ the same polynomial order for velocity and pressure, which requires the use of stabilisation techniques to compensate for the inf-sup deficiency of suchpairs. In the present work, we extend to the space-time formulation the idea of the popular Taylor-Hood element for the (Navier-)Stokes equations. By using quadratic interpolation for velocities and linear for pressure, in both space and time, we attain a stable finite element method which provides optimal convergence for pressure, velocity and stresses.

Cite as:

Pacheco, D. R. Q., & Steinbach, O. (2019). Space-time Taylor-Hood elements for incompressible flows. Computer Methods in Materials Science, 19(2), 64-69.

Article (PDF):


Computational Fluid Dynamics, Finite Element Method, Space-time methods, Incompressible flows, Stable finite elements


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