Mathematical Theory of Finite Elements
Author: Leszek F. Demkowicz (Author)
Publisher finelybook 出版社: SIAM – Society for Industrial and Applied Mathematics
Publication Date 出版日期: 2023-09-22
Language 语言: English
Print Length 页数: 216 pages
ISBN-10: 161197772X
ISBN-13: 9781611977721
Book Description
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. Intended for graduate students in computational science, engineering, and mathematics programs, Mathematical Theory of Finite Elements is also appropriate for graduate mathematics and mathematically oriented engineering students. Instructors will find the book useful for courses in real analysis, functional analysis, energy (Sobolev) spaces, and Hilbert space methods for PDEs.
About the Author
Leszek F. Demkowicz is assistant director of the Oden Institute for Computational Engineering and Sciences, holder of the W. A. ”Tex” Moncrief Jr. Chair in Computational Engineering and Sciences II, and professor in the Department of Aerospace Engineering and Engineering Mechanics and the department of mathematics at The University of Texas at Austin. He has authored and co-authored more than 220 articles and several books. He co-invented, with Jay Gopalakrishnan of Portland State University, the discontinuous Petrov–Galerkin method. The recipient of several awards, he is a Fellow of both IACM and USACM, an honorary member of PACM, and a foreign member of the Polish Academy of Arts and Sciences. His scientific interests include numerical analysis, adaptive finite element methods, wave propagation problems, including acoustics, elastodynamics and electromagnetics, and computational fluid dynamics.
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