Numerical Analysis RIT (fall 2007)

Focus on Numerics for PDE Room: 1311 Time: 4:30--5:30 p.m

Lecture I: A posteriori error estimates for time-dependent Stokes

• by Clarence V. Baney


• This is recent work by Makridakis and a former student of Ricardo, who now works with E. Baensch (Erlangen, Germany)

Lecture II: Computational parametric Willmore flow

• by Andrea Bonito


• This is a recent work by G. Dziuk (submitted). In this paper, a new derivation of the first variation of the Willmore Energy is proposed. The latter does not require any integration by parts (compare to Rusu 2005, Interface and Free Boundaries) and therefore a stability estimate is easily obtained.

• Monday September 10th: introduction and proof of the final result
• Monday September 17th: proof of the two intermediate lemmas and computational results. Note that the time is exceptionally 3:30pm!

Lecture III: On the construction of suitable weak solutions to the 3D Navier-Stokes equations and open related questions.

• by J-L Guermond.

• Monday November 5th: Prof. Jean-Luc Guermond will discuss his recent progress.

Lecture IV: Short time existence of solution to the Navier-Stokes system coupled with Willmore boundary force.

• by A. Cheng.

• November 7th: Arthur will disscuss his recent progress.
• November 12h: Arthur will continue the disscussion

Lecture V: Operator-valued semigroup.

• by A. Bonito.

• December 3rd: I will discuss basic notions of semigroup theory. Starting from the abstract Cauchy problems I will define the main tools to obtain the maximal regularity property. Application to Stokes and Navier-Stokes.