Mathematical theory of finite elements

By:

Demkowicz, Leszek F

Series: Computational Science & Engineering ; Vol. 28Publication details: Philadelphia: Society for Industrial and Applied Mathematics, 2024.Description: xi, 176 p.: col. ill.; pbk.: 25 cmISBN:

9781611977721

Subject(s):

DDC classification:

518.25 DEM

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 Lax-Milgram theorem and Cea's lemma to the Babuska theorem and Brezzi's theory. He finishes with an introduction to the discontinuous Petrov-Galerkin (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 grad-curl-div sequence, and an introduction to the DPG method. https://epubs.siam.org/doi/book/10.1137/1.9781611977738

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Item type	Current library	Collection	Call number	Copy number	Status	Barcode
Books	IIT Gandhinagar	General	518.25 DEM (Browse shelf(Opens below))	1	Available	035838

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Includes Bibliographical References and Index

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 Lax-Milgram theorem and Cea's lemma to the Babuska theorem and Brezzi's theory. He finishes with an introduction to the discontinuous Petrov-Galerkin (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 grad-curl-div sequence, and an introduction to the DPG method.

https://epubs.siam.org/doi/book/10.1137/1.9781611977738

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