Least-Squares Finite Element Methods

1. Auflage 2009
ISBN: 978-0-387-68922-7
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 660 Seiten

Since their emergence, finite element methods have taken a place as one of the most versatile and powerful methodologies for the approximate numerical solution of Partial Differential Equations. These methods are used in incompressible fluid flow, heat, transfer, and other problems. This book provides researchers and practitioners with a concise guide to the theory and practice of least-square finite element methods, their strengths and weaknesses, established successes, and open problems.

Autoren/Hrsg.

Inhaltsverzeichnis

1;Preface;7
2;Contents;15
3;Part I Survey of Variational Principles and Associated Finite Element Methods;23
3.1;Classical Variational Methods;24
3.2;Alternative Variational Formulations;55
4;Part II Abstract Theory of Least-Squares Finite Element Methods;86
4.1;Mathematical Foundations of Least-Squares Finite Element Methods;87
4.2;The Agmon–Douglis–Nirenberg Setting for Least-Squares Finite Element Methods;120
5;Part III Least-Squares Finite Element Methods for Elliptic Problems;148
5.1;Scalar Elliptic Equations;149
5.2;Vector Elliptic Equations;213
5.3;The Stokes Equations;253
6;Part IV Least-Squares Finite Element Methods for Other Settings;325
6.1;The Navier–Stokes Equations;326
6.2;Parabolic Partial Differential Equations;381
6.3;Hyperbolic Partial Differential Equations;417
6.4;Control and Optimization Problems;443
6.5;Variations on Least-Squares Finite Element Methods;489
7;Part V Supplementary Material;545
7.1;Analysis Tools;546
7.2;Compatible Finite Element Spaces;565
7.3;Linear Operator Equations in Hilbert Spaces;597
7.4;The Agmon–Douglis–Nirenberg Theory and Verifying its Assumptions;604
8;References;636
9;Acronyms;652
10;Glossary;653
11;Index;656