This talk will be in the originally intended format for this seminar series, namely, "the cool thing that I'm working on this week."

I will discuss, briefly, the semi-implicit timestepping used in our fluid dynamics code, Nek5000, and the impact that this has when one moves from the "classic" formulation to more sophisitcated options.

For background, I'll present basic accuracy and stability considerations for the semi-implicit formulation we use and how one can retain this approach, with the same ccuracy, stability, and cost for more sophisticated (e.g., nonlinear) operators. This development has also led to an interesting observation in stabilizing high-order BDF schemes, which is new (to me).

The level of the talk will be Num. Anal. 101.