Finite element approximations of Burgers' equation

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.

Name thesis:degree_name

Master of Science

Level thesis:degree_level

masters

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

1995

Author dc:creator

• Pugh, Steven M.

Chair dc:contributor.committeechair

• Burns, John A.

Committee members dc:contributor.committeemember

• Cliff, Eugene M.
• Herdman, Terry L.

• finite elements
• Burgers equation

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Language dc:language.iso

en

Dc Identifier Other

etd-12052009-020403

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/35977