Good morning,

Colleagues in the Analysis section have organized this seminar by Alex Kaltenbach that may be of interest to some of us. The detailed information follows.

Best,

Fabio

Speaker: Alex Kaltenbach, Technische Universität Berlin

Seminar: A finite element approximation of a simplified model for smart fluids: an error analysis

Date: October 9th at 5:00 pm, Aula Riunioni (Maths Department)

Abstract: In this talk, a finite element approximation of the steady $p(\cdot)$-Navier--Stokes equations ($p(\cdot)$ is variable dependent) is examined for orders of convergence by assuming natural fractional regularity assumptions on the velocity vector field and the kinematic pressure. Numerical experiments confirm the quasi-optimality of the \textit{a priori} error estimates (for the velocity).

The steady $p(\cdot)$-Navier--Stokes equations are a prototypical example of a non-linear system with variable growth conditions. They appear naturally in physical models for so-called \textit{smart fluids}, \textit{e.g.}, electro-rheological fluids, micro-polar electro-rheological fluids, magneto-rheological fluids, chemically reacting fluids, and thermo-rheological fluids, and have the potential for an application in numerous areas, \textit{e.g.}, in electronic, automobile, heavy machinery, military, and biomedical industry.