Authors: Aczon, Melissa D. (2006)We have two main objectives in this dissertation: (i) to analyze the splitting mechanism behind entropy stable finite difference approximations of conservative systems; and (ii) to investigate global error estimation for nonlinear, hyperbolic partial differential equations.
For symmetrizable systems of conservation laws, Olsson used entropy functions to obtain rigorous stability estimates for a family of finite difference schemes that approximate the original equations [Ols95c]. A key element behind the estimates and the resulting schemes is a splitting process which uses an entropy function to recast the flux derivative into a skew-symmetric form. Gerritsen applied the splitting concept to the compressible Euler equations [Ger96a].
We studied the splitting process through a param...