Degree Type

Dissertation

Date of Award

2003

Degree Name

Doctor of Philosophy

Department

Mathematics

First Advisor

Max Gunzburger

Abstract

It is well known that the classic Galerkin finite-element method is unstable when applied to hyperbolic conservation laws, such as the Euler equations for compressible flow. Adding a diffusion term to the equations stabilizes the method but sacrifices too much accuracy to be of any practical use. An elegant solution devised by Eitan Tadmor for spectral methods is to add diffusion only to the high frequency modes of the solution, which stabilizes the method without the sacrifice of accuracy. We incorporate this idea into the finite-element framework by using hierarchical functions as a multi-frequency basis. The result is a new finite element method for solving hyperbolic conservation laws. For this method, we are able to prove convergence for a one-dimensional scalar conservation Law; Numerical results are presented for one- and two-dimensional hyperbolic conservation laws.

DOI

https://doi.org/10.31274/rtd-180813-9890

Publisher

Digital Repository @ Iowa State University, http://lib.dr.iastate.edu

Copyright Owner

Marcus Calhoun-Lopez

Language

en

Proquest ID

AAI3105069

File Format

application/pdf

File Size

107 pages

Included in

Mathematics Commons

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