Tel-Aviv University
School of Mathematical Sciences
Department of Applied Mathematics

Applied Mathematics Seminar


Tuesday, March 1st, 2011

Schreiber 309, 15:10



Dalia Fishelov

Afeka-Tel-Aviv Academic College of Engineering

Optimal convergence of a fourth-order compact scheme for the biharmonic problem

Abstract:

We present a fourth-order approximation of the biharmonic problem in the one-dimensional case and prove its optimal (fourth-order) convergence to the exact solution for non-periodic boundary conditions. The discrete set of eigenfunctions and eigenvalues are calculated and presented.

We also present a high-order compact scheme for the biharmonic equation and study its accuracy and stability properties.

Similar such approximations are derived for the two-dimensional Navier-Stokes equations. Numerical results indicate the existence of periodic solutions for high Reynolds number.

Joint work with M. Ben-Artzi and J.-P. Croisille