Dual-Primal Isogeometric Tearing and Interconnecting (IETI) Methods for the Stokes problem

Dr. Stefan Takacs

Nov. 16, 2021, 3:30 p.m. S3 048

In this talk, we discuss the discretization Stokes equations using
multi-patch Isogeometric Analysis. We consider the Stokes equations in
its mixed formulation, which has saddle point structure. Well-posedness
of the (discretized) Stokes system is usually shown by means of Brezzi's
theorem. Besides the conditions that carry over from the (well studied)
continuous case, there is one condition that has to be verified
separately for the discretized problem: the inf-sup condition. For
discretizations with single-patch Isogeometric Analysis, the inf-sup
condition has already been shown for several discretizations. We base
our considerations on the isogeometric Taylor-Hood element and its
analysis by Bressan and Sangalli. In the talk we will see, how inf-sup
results for single-patch case can be carried over to the multi-patch
case. We will rediscover that the inf-sup constant heavily depends on
the global geometry. Then, we will discuss the efficient solution of the
problem by means of a domain decomposition method, namely the IETI
method. We will be very careful to avoid the global inf-sup constant.
The numerical experiments confirm that we succeeded with this attempt.