Date:
Wed, 11/12/201912:00-13:00
Location:
Ross 70
Title: Spline functions, the biharmonic operator and approximate
eigenvalues.
Abstract: The biharmonic operator plays a central role in a wide array of physical models, such as elasticity theory and the streamfunction formulation of the Navier-Stokes equations.In this talk a full discrete elliptic calculus is presented. The primary object of this calculus is a high-order compact discrete biharmonic operator (DBO).
It turns out that there is a strong connection between cubic spline functions (on an interval) and the DBO. In particular, the (scaled) fourth-order distributional derivative of the cubic spline is identical to the action of the DBO on grid functions. It allows an explicit expression for the kernel of the inverse of the DBO.
Finally, as an important application, we prove the optimal convergence of the eigenvalues.
Joint work with G. Katriel.
eigenvalues.
Abstract: The biharmonic operator plays a central role in a wide array of physical models, such as elasticity theory and the streamfunction formulation of the Navier-Stokes equations.In this talk a full discrete elliptic calculus is presented. The primary object of this calculus is a high-order compact discrete biharmonic operator (DBO).
It turns out that there is a strong connection between cubic spline functions (on an interval) and the DBO. In particular, the (scaled) fourth-order distributional derivative of the cubic spline is identical to the action of the DBO on grid functions. It allows an explicit expression for the kernel of the inverse of the DBO.
Finally, as an important application, we prove the optimal convergence of the eigenvalues.
Joint work with G. Katriel.