On fully discrete Galerkin approximations for the incompressible Navier-Stokes equations

Author

Theodoros Katsaounis

Date of Award

8-1994

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Mathematics

Major Professor

O. Karakashian

Committee Members

Steven Serbin, Vasilios Alexiades, Xiaobing Feng, Michael Berry

Abstract

Fully discrete approximations to the solution of the Incompressible Navier-Stokes equations are introduced and analyzed. Implicit Runge-Kutta methods are used for the temporal discretizations. Standard elements are used for the pressure approximation, while non-conforming finite element spaces are used for the velocity approximation. These elements are discontinuous across interelement boundaries and satisfy the incompressibility condition pointwise on each "trian-gle". Furthermore, no global quasi-uniformity condition is required from the sub-divisions of the domain. Newton's method and a more efficient Implicit-Explicit scheme are employed to solve the resulting system of nonlinear equations. Numer-ical solutions to two well known physical benchmark problems are presented.

Recommended Citation

Katsaounis, Theodoros, "On fully discrete Galerkin approximations for the incompressible Navier-Stokes equations. " PhD diss., University of Tennessee, 1994.
https://trace.tennessee.edu/utk_graddiss/10385