Title page for ETD etd-12052009-020403


Type of Document Master's Thesis
Author Pugh, Steven M.
URN etd-12052009-020403
Title Finite element approximations of Burgers' equation
Degree Master of Science
Department Mathematics
Advisory Committee
Advisor Name Title
Burns, John A. Committee Chair
Cliff, Eugene M. Committee Member
Herdman, Terry L. Committee Member
Keywords
  • finite elements
  • Burgers equation
Date of Defense 1995-09-01
Availability unrestricted
Abstract
This work is a numerical study of Burgers' equation with Neumann boundary conditions. The goal is to determine the long term behavior of solutions. We develop and test two separate finite element and Galerkin schemes and then use those schemes to compute the response to various initial conditions and Reynolds numbers.

It is known that for sufficiently small initial data, all steady state solutions of Burgers' equation with Neumann boundary conditions are constant. The goal here is to investigate the case where initial data is large. Our numerical results indicate that for certain initial data the solution of Burgers' equation can approach non-constant functions as time goes to infinity. In addition, the numerical results raise some interesting questions about steady state solutions of nonlinear systems.

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