Least-squares finite element methods

✍ Scribed by Bochev P., Gunzburger M.

• Publisher: Springer
• Year: 2009
• Tongue: English
• Leaves: 664
• Series: Applied Mathematical Sciences
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Cover......Page 2
Preface......Page 7
Contents......Page 15
Ch 1 Classical Variational Methods......Page 23
Ch 2 Alternative Variational Formulations......Page 54
Ch 3 Mathematical Foundations of Least-Squares Finite Element Methods......Page 85
Ch 4 The Agmon–Douglis–Nirenberg Setting......Page 118
Ch 5 Scalar Elliptic Equations......Page 146
Ch 6 Vector Elliptic Equations......Page 210
Ch 7 The Stokes Equations......Page 250
Ch 8 The Navier–Stokes Equations......Page 322
Ch 9 Parabolic Partial Differential Equations......Page 377
Ch 10 Hyperbolic Partial Differential Equations......Page 413
Ch 11 Control and Optimization Problems......Page 439
Ch 12 Variations on Least-Squares Finite Element Methods......Page 485
App A Analysis Tools......Page 541
App B Compatible Finite Element Spaces......Page 560
App C Linear Operator Equations in Hilbert Spaces......Page 592
App D The Agmon–Douglis–Nirenberg Theory and Verifying its Assumptions......Page 599
References......Page 631
Acronyms......Page 647
Glossary......Page 648
Index......Page 651