BCAM Scientific Seminar: A mass conserving mixed stress formulation for incompressible flows

Date: Tue, May 29 2018

Hour: 16:00

Speakers: Philip Lukas Lederer

*Note that this seminar will be at Mazarredo 16 instead of BCAM's Seminar Room. 

One of the main difficulties in computational fluid dynamics lies in the proper treatment of the incompressibility condition. A weak treatment of this constraint can lead to a locking phenomena if the viscosity is small and results in bad velocity approximations. Recent developments show that H(div)-conforming finite elements for the approximation of the velocity provide major benefits such as exact mass conservation, pressure-independent (locking free) and polynomial robust error estimates. By introducing a new variable which approximates the gradient of an H(div)- conforming velocity we derive a new mixed stress formulation of the incompressible Stokes equations. For the analysis a new function space, the H(curldiv), is defined, in which we can show well posedness.

In the discrete setting two different approaches lead to a stable analysis. We present the construction of proper Finite elements, discuss solvability and verify our method with several numerical examples. We conclude the talk by a further motivation of the new formulation: the numerical treatment of a linearized R13 model.


Institute for Analysis an Scientific Computing - TU Wien (Austria)

Confirmed speakers:

Philip Lukas Lederer