Mathematical theory of finite elements
 Responsibility
 Leszek F. Demkowicz.
 Publication
 Philadelphia, Pennsylvania : Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104) ; Alexandria, Virginia : American Statistical Association, [2023]
 Physical description
 1 PDF (xi, 204 pages).
 Series
 Computational science and engineering.
Online
More options
Description
Creators/Contributors
 Author/Creator
 Demkowicz, Leszek, author.
 Contributor
 Society for Industrial and Applied Mathematics, publisher.
Contents/Summary
 Bibliography
 Includes bibliographical references (pages 197200) and index.
 Contents

 Preliminaries
 Coercivity
 Conforming elements and interpolation theory
 Beyond coercivity
 The DPG method.
 Summary
 This book discusses the foundations of the mathematical theory of finite element methods. The focus is on two subjects: the concept of discrete stability, and the theory of conforming elements forming the exact sequence. Both coercive and noncoercive problems are discussed. Following the historical path of development, the author covers the Ritz and Galerkin methods to Mikhlin's theory, followed by the LaxMilgram theorem and Cea's lemma to the Babuska theorem and Brezzi's theory. He finishes with an introduction to the discontinuous PetrovGalerkin (DPG) method with optimal test functions. Based on the author's personal lecture notes for a popular version of his graduate course on mathematical theory of finite elements, the book includes a unique exposition of the concept of discrete stability and the means to guarantee it, a coherent presentation of finite elements forming the exact gradcurldiv sequence, and an introduction to the DPG method.
Subjects
 Subjects
 Finite element method.
 MATHEMATICS / Applied.
 MATHEMATICS / Differential Equations / Partial.
 MATHEMATICS / Functional Analysis.
 MATHEMATICS / Mathematical Analysis.
 MATHEMATICS / Numerical Analysis.
 COMPUTERS / Computer Simulation.
 SCIENCE / Acoustics & Sound.
 SCIENCE / Mechanics / General.
 SCIENCE / Mechanics / Solids.
 SCIENCE / Physics / Electromagnetism.
 SCIENCE / Physics / Mathematical & Computational.
 finite elements
 numerical analysis
 PetrovGalerkin method
 exact sequence conforming elements
 Babuska's theorem
 Ritz method
 asymptotic stability
 mixed methods
 DPG method
 noncoercive problems
 LaxMilgram theorem
 Brezzi's theory
 variational formulations
 ultraweak variational formulation
 broken test spaces
 BrambleHilbert lemma
 BabuskaNecas theorem
 interpolation theory
 hierarchical shape functions
 orientationembedded shape functions
 interpolation error estimates
 a priori error estimation
 Cea's Lemma
 Mikhlin's theory
Bibliographic information
 Publication date
 2023
 Series
 Computational science & engineering
 Access
 Restricted to subscribers or individual electronic text purchasers.
 Note
 Also available in print version.
 Format
 Mode of access: World Wide Web.
 System requirements: Adobe Acrobat Reader.
 ISBN
 9781611977738 electronic
 9781611977721 print
 Publisher number
 CS28 SIAM