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Finite Elements I : Approximation and Interpolation /

This book is the first volume of a three-part textbook suitable for graduate coursework, professional engineering and academic research. It is also appropriate for graduate flipped classes. Each volume is divided into short chapters. Each chapter can be covered in one teaching unit and includes exer...

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Bibliographic Details
Main Authors: Ern, Alexandre (Author), Guermond, Jean-Luc (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Cham : Springer International Publishing : Imprint: Springer, 2021.
Edition:1st ed. 2021.
Series:Texts in Applied Mathematics, 72
Subjects:
Partial differential equations.
Functional analysis.
Partial Differential Equations.
Functional Analysis.
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • Part I: Elements of Functional Analysis
  • Lebesgue spaces
  • Weak derivatives and Sobolev spaces
  • Traces and PoincarĂ© Inequalities
  • Duality in Sobolev spaces
  • Part II: Introduction to Finite Elements
  • Main ideas and definitions
  • One-dimensional finite elements and tensorization
  • Simplicial finite elements
  • Part III: Finite element interpolation
  • Meshes
  • Finite element generation
  • Mesh orientation
  • Local interpolation on affine meshes
  • Local inverse and functional inequalities
  • Local interpolation on non-affine meshes
  • H(div) finite elements
  • H(curl) finite elements
  • Local interpolation in H(div) and H(curl) (I)
  • Local interpolation in H(div) and H(curl) (II)
  • Part IV: Finite element spaces
  • From broken to conforming spaces
  • Main properties of the conforming spaces
  • Face gluing
  • Construction of the connectivity classes
  • Quasi-interpolation and best approximation
  • Commuting quasi-interpolation
  • Appendices
  • Banach and Hillbert spaces
  • Differential calculus.