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-Universit├Ąt 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.