[Dottorcomp] Seminari di Matematica Applicata, 20/02/2024, Christian Kreuzer.

[Stefano Lisini]

Seminari di Matematica Applicata, Dipartimento di Matematica "F. Casorati"
e Istituto del CNR IMATI "E. Magenes" di Pavia.

Martedì 20 febbraio 2024, alle ore 16.00 precise, presso la sala conferenze
dell'IMATI-CNR di Pavia,

Christian Kreuzer (TU Dortmund)terrà un seminario dal titolo:

Pressure robust discretisations of the nonlinear Stokes equations.

Abstract.
For standard conforming finite element methods for the power law Stokes
problem suboptimal convergence rates are observed theoretically and in
simulations, for exponents r>2. The reason for this lies in the interaction
of the velocity and the pressure error together with some mismatch of their
respective error measures. In a recent series of papers together with
Pietro Zanotti and Rüdiger Verfürth, we have developed pressure robust and
quasi optimal variants of some standard Stokes elements. Here one main
feature is that the velocity error is fully decoupled from the pressure
error. We shall demonstrate for the Crouzeix-Raviart first order velocities
with piecewise constant pressure, that the developed pressure robust
techniques can be used to remedy the suboptimal approximation results for
nonlinear Stokes problems. In particular, we prove first order convergence
of the velocity error in the quasi-norm independently of the exponent r. A
discussion of several extensions to symmetric stresses and quadratic
velocity approximations complete the talk. This is a joint work with Lars
Diening, Adrian Hirn, and Pietro Zanotti.

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