This book discusses the foundations of the mathematical theory of finite element methods. The focus is on the concept of discrete stability and the exact sequence conforming elements and covers both coercive and non-coercive problems. Following a historical path of development, the author covers the Ritz and the Galerkin methods to Mikhlin's theory, the Lax-Milgram theorem and Cea's lemma to the Babuska theorem and Brezzi's theory, and finishes with an introduction to the discontinuous Petrov-Galerkin method with optimal test functions.
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. The book is appropriate for courses in real analysis, functional analysis, energy (Sobolev) spaces, and Hilbert space methods for PDEs.
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978-1-61197-772-1 (9781611977721)
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Schweitzer Klassifikation
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, 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 over 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.
