Mathematical Theory of Finite Elements

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Mathematical Theory of Finite Elements is written by Leszek Demkowicz and published by Society for Industrial and Applied Mathematics (SIAM). It's available with International Standard Book Number or ISBN identification 161197772X (ISBN 10) and 9781611977721 (ISBN 13).

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.