# Jerusalem Mathematics Colloquium

Thursday, 22nd May 2008, 4:00 pm

Mathematics Building, Lecture Hall 2

##

Itai Horev

(HU)

"From Navier-Stokes to the biharmonic equation in planar irregular
domains"

** Abstract: **The biharmonic equation is of great importance in many fields of applied
mathematics. In particular, the classical (Lagrange , 1768)
streamfunction formulation of flow problems involves the biharmonic
operator as the highest-order term. We give a brief review of the
Navier-Stokes theory. We then present a finite difference scheme
which approximates
the biharmonic equation in general two-dimensional irregular domains. The
scheme includes discretizing the values of the function and its
derivatives at grid points, and then studying a class of interpolations by
sixth-order polynomials. The main interest is that it allows to
construct the time-dependent solver, which fits closely to the pure
streamfunction formulation of the Navier-Stokes equation.

Light refreshments will be served in the faculty lounge at
3:30.

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