Least-Squares Finite Element Methods

  • Max D. Gunzburger
  • Pavel B. Bochev

Part of the Applied Mathematical Sciences book series (AMS, volume 166)

Table of contents

  1. Front Matter
    Pages 1-21
  2. Survey of Variational Principles and Associated Finite Element Methods.

    1. Front Matter
      Pages 1-1
    2. Pavel B. Bochev, Max D. Gunzburger
      Pages 1-31
    3. Pavel B. Bochev, Max D. Gunzburger
      Pages 1-31
  3. Abstract Theory of Least-Squares Finite Element Methods

    1. Front Matter
      Pages 1-1
    2. Pavel B. Bochev, Max D. Gunzburger
      Pages 1-33
  4. Least-Squares Finite Element Methods for Elliptic Problems

    1. Front Matter
      Pages 1-1
    2. Pavel B. Bochev, Max D. Gunzburger
      Pages 1-64
    3. Pavel B. Bochev, Max D. Gunzburger
      Pages 1-40
    4. Pavel B. Bochev, Max D. Gunzburger
      Pages 1-72
  5. Least-Squares Finite Element Methods for Other Settings

    1. Front Matter
      Pages 1-1
    2. Pavel B. Bochev, Max D. Gunzburger
      Pages 1-55
    3. Pavel B. Bochev, Max D. Gunzburger
      Pages 1-36
    4. Pavel B. Bochev, Max D. Gunzburger
      Pages 1-26
    5. Pavel B. Bochev, Max D. Gunzburger
      Pages 1-46
    6. Pavel B. Bochev, Max D. Gunzburger
      Pages 1-56
  6. Supplementary Material

    1. Front Matter
      Pages 1-1
    2. Pavel B. Bochev, Max D. Gunzburger
      Pages 1-19
    3. Pavel B. Bochev, Max D. Gunzburger
      Pages 1-32

About this book

Introduction

The book examines theoretical and computational aspects of least-squares finite element methods(LSFEMs) for partial differential equations (PDEs) arising in key science and engineering applications. It is intended for mathematicians, scientists, and engineers interested in either or both the theory and practice associated with the numerical solution of PDEs.

The first part looks at strengths and weaknesses of classical variational principles, reviews alternative variational formulations, and offers a glimpse at the main concepts that enter into the formulation of LSFEMs. Subsequent parts introduce mathematical frameworks for LSFEMs and their analysis, apply the frameworks to concrete PDEs, and discuss computational properties of resulting LSFEMs. Also included are recent advances such as compatible LSFEMs, negative-norm LSFEMs, and LSFEMs for optimal control and design problems. Numerical examples illustrate key aspects of the theory ranging from the importance of norm-equivalence to connections between compatible LSFEMs and classical-Galerkin and mixed-Galerkin methods.

Pavel Bochev is a Distinguished Member of the Technical Staff at Sandia National Laboratories with research interests in compatible discretizations for PDEs, multiphysics problems, and scientific computing.

Max Gunzburger is Frances Eppes Professor of Scientific Computing and Mathematics at Florida State University and recipient of the W.T. and Idelia Reid Prize in Mathematics from the Society for Industrial and Applied Mathematics.

 

Keywords

Analysis Bochev Elements Finite Least-Squares finite element method hyperbolic partial differential equation linear optimization operator optimization

Authors and affiliations

  • Max D. Gunzburger
  • Pavel B. Bochev

There are no affiliations available

Bibliographic information

  • DOI https://doi.org/10.1007/b13382
  • Copyright Information Springer-Verlag New York 2009
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-387-30888-3
  • Online ISBN 978-0-387-68922-7
  • Series Print ISSN 0066-5452
  • About this book