**Date & Time:** Monday, October 15, 2012, 16:00-16:40.

**Venue:** Ramanujan Hall

**Title:**Quasi Optimal Adaptive Pseudostress Approximation of the Stokes
Equations

**Speaker: ** Prof. Dietmar Gallistl

Humboldt-Universität zu Berlin

**Abstract:** The pseudostress-velocity formulation of the stationary Stokes problem
allows some
quasi-optimal Raviart-Thomas mixed finite element formulation for any
polynomial degree.
The adaptive algorithm employs standard residual-based explicit a
posteriori error estimation from
Carstensen, Kim, Park [SIAM J. Numer. Anal. 2012] for the lowest-order
Raviart-Thomas finite element functions in a simply connected Lipschitz
domain. This talk presents optimal convergence rates in terms of the
number of unknowns of the adaptive mesh-refining algorithm for the
lowest-order case
based on the concept of approximation classes. The proofs use some novel
equivalence to first-order
nonconforming Crouzeix-Raviart discretisation plus a particular
Helmholtz decomposition of deviatoric tensors.