Computation and Visualization of Geometric Partial Differential Equations

Computation and Visualization of Geometric Partial Differential Equations
Author :
Publisher : Lulu.com
Total Pages : 304
Release :
ISBN-10 : 9781329440739
ISBN-13 : 1329440730
Rating : 4/5 (730 Downloads)

Book Synopsis Computation and Visualization of Geometric Partial Differential Equations by : Christopher Tiee

Download or read book Computation and Visualization of Geometric Partial Differential Equations written by Christopher Tiee and published by Lulu.com. This book was released on 2015-08-09 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 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.


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