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The Least-Squares Finite Element Method

Theory and Applications in Computational Fluid Dynamics and Electromagnetics

  • Book
  • © 1998

Overview

Authors:
  1. Bo-nan Jiang

    1. Institute for Computational Methods in Propulsion, NASA Lewis Research Center, Cleveland, USA

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  • This is the first monograph on the LSFEM method
  • It treats Navier-Stokes and Maxwell equations in one and the same book

Part of the book series: Scientific Computation (SCIENTCOMP)

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Table of contents (15 chapters)

  1. Front Matter

    Pages I-XVI
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  2. Basic Concepts of LSFEM

    1. Front Matter

      Pages 1-1
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    2. Introduction

      • Bo-nan Jiang
      Pages 3-10

    3. First-Order Scalar Equation in One Dimension

      • Bo-nan Jiang
      Pages 11-30

    4. First-Order System in One Dimension

      • Bo-nan Jiang
      Pages 31-44

  3. Fundamentals of LSFEM

    1. Front Matter

      Pages 45-45
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    2. Basis of LSFEM

      • Bo-nan Jiang
      Pages 47-79

    3. Div—Curl System

      • Bo-nan Jiang
      Pages 81-95

    4. Div—Curl—Grad System

      • Bo-nan Jiang
      Pages 97-112

  4. LSFEM in Fluid Dynamics

    1. Front Matter

      Pages 113-113
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    2. Inviscid Irrotational Flows

      • Bo-nan Jiang
      Pages 115-128

    3. Incompressible Viscous Flows

      • Bonan Jiang
      Pages 129-199

    4. Convective Transport

      • Bo-nan Jiang
      Pages 201-240

    5. Incompressible Inviscid Rotational Flows

      • Bo-nan Jiang
      Pages 241-257

    6. Low-Speed Compressible Viscous Flows

      • Bo-nan Jiang
      Pages 259-284

    7. Two-Fluid Flows

      • Bo-nan Jiang
      Pages 285-302

    8. High-Speed Compressible Flows

      • Bo-nan Jiang
      Pages 303-328

  5. LSFEM in Electromagnetics

    1. Front Matter

      Pages 329-329
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    2. Electromagnetics

      • Bo-nan Jiang
      Pages 331-382

  6. Solution of Discrete Equations

    1. Front Matter

      Pages 383-383
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Keywords

About this book

Here is a comprehensive introduction to the least-squares finite element method (LSFEM) for numerical solution of PDEs. It covers the theory for first-order systems, particularly the div-curl and the div-curl-grad system. Then LSFEM is applied systematically to 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. LSFEM is simple, efficient and robust, and can solve a wide range of problems in fluid dynamics and electromagnetics, including incompressible viscous flows, rotational inviscid flows, low-Mach-number compressible flows, two-fluid and convective flows, scattering waves, etc.

Authors and Affiliations

  • Institute for Computational Methods in Propulsion, NASA Lewis Research Center, Cleveland, USA

    Bo-nan Jiang

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