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The Least-Squares Finite Element Method

Theory and Applications in Computational Fluid Dynamics and Electromagnetics

  • Bo-nan Jiang

Part of the Scientific Computation book series (SCIENTCOMP)

Table of contents

  1. Front Matter
    Pages I-XVI
  2. Basic Concepts of LSFEM

    1. Front Matter
      Pages 1-1
    2. Bo-nan Jiang
      Pages 3-10
    3. Bo-nan Jiang
      Pages 31-44
  3. Fundamentals of LSFEM

    1. Front Matter
      Pages 45-45
    2. Bo-nan Jiang
      Pages 47-79
    3. Bo-nan Jiang
      Pages 81-95
    4. Bo-nan Jiang
      Pages 97-112
  4. LSFEM in Fluid Dynamics

    1. Front Matter
      Pages 113-113
    2. Bo-nan Jiang
      Pages 115-128
    3. Bonan Jiang
      Pages 129-199
    4. Bo-nan Jiang
      Pages 201-240
    5. Bo-nan Jiang
      Pages 241-257
    6. Bo-nan Jiang
      Pages 259-284
    7. Bo-nan Jiang
      Pages 285-302
    8. Bo-nan Jiang
      Pages 303-328
  5. LSFEM in Electromagnetics

    1. Front Matter
      Pages 329-329
    2. Bo-nan Jiang
      Pages 331-382
  6. Solution of Discrete Equations

    1. Front Matter
      Pages 383-383
  7. Back Matter
    Pages 397-418

About this book

Introduction

This is the first book devoted to the least-squares finite element method (LSFEM), which is a simple, efficient and robust technique for the numerical solution of partial differential equations. The book demonstrates that the LSFEM can solve a broad range of problems in fluid dynamics and electromagnetics with only one mathematical/computational formulation. The book shows that commonly adopted special treatments in computational fluid dynamics and computational electromagnetics, such as upwinding, numerical dissipation, staggered grid, non-equal-order elements, operator splitting and preconditioning, edge elements, vector potential, and so on, are unnecessary.
This book introduces the basic theory of the least-squares method for first-order PDE systems, particularly the div-curl system and the div-curl-grad system. It is applied to the study of permissible boundary conditions for the incompressible Navier--Stokes equations, to show that the divergence equations in the Maxwell equations are not redundant, and to derive equivalent second-order versions of the Navier--Stokes equations and the Maxwell equations. This book covers diverse applications such as incompressible viscous flows, rotational inviscid flows, low- or high-Mach-number compressible flows, two-fluid flows, convective flows, and scattering waves.

Keywords

CEM CFD Finite Element Method First-Order System Least Squares Maxwell's equations Navier-Stokes equation Numerical Analysis Partial Differential Equations computational electrodynamics computational fluid dynamics differential equation fluid dynamics numerical dissipation

Authors and affiliations

  • Bo-nan Jiang
    • 1
  1. 1.Institute for Computational Methods in PropulsionNASA Lewis Research CenterClevelandUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-03740-9
  • Copyright Information Springer-Verlag Berlin Heidelberg 1998
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-08367-9
  • Online ISBN 978-3-662-03740-9
  • Series Print ISSN 1434-8322
  • Buy this book on publisher's site
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