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
Copyright Date
2003
Language
en
Proquest ID
AAI3105069
File Format
application/pdf
File Size
107 pages
Recommended Citation
Calhoun-Lopez, Marcus, "Numerical solutions of hyperbolic conservation laws: incorporating multi-resolution viscosity methods into the finite element framework " (2003). Retrospective Theses and Dissertations. 1426.
https://lib.dr.iastate.edu/rtd/1426
