Computation and Visualization of Geometric Partial Differential Equations
Author: Christopher Tiee
Publisher: Lulu.com
Published: 2015-08-09
Total Pages: 304
ISBN-13: 1329440730
DOWNLOAD EBOOKThis is an extended version of my PhD thesis which extends the theory of finite element exterior calculus (FEEC) to parabolic evolution equations. In the extended version, I explore some more precise visualizations of the defined quantities, as well as explain how the modern theory of functional analysis applies. In the main part, I extend the theory of approximating evolution equations in Euclidean space (using FEEC) to hypersurfaces. After these main results, I describe some possible extensions to nonlinear equations. A few appendices detail one of the original motivations for getting into this theory in the first place: canonical geometries given as steady state solutions and extremals of certain functionals.