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AuthorErn, Alexandre. author
TitleTheory and Practice of Finite Elements [electronic resource] / by Alexandre Ern, Jean-Luc Guermond
ImprintNew York, NY : Springer New York : Imprint: Springer, 2004
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Descript XIV, 526 p. online resource


This book presents the mathematical theory of finite elements, starting from basic results on approximation theory and finite element interpolation and building up to more recent research topics, such as and Discontinuous Galerkin, subgrid viscosity stabilization, and a posteriori error estimation. The body of the text is organized into three parts plus two appendices collecting the functional analysis results used in the book. The first part develops the theoretical basis for the finite element method and emphasizes the fundamental role of inf-sup conditions. The second party addresses various applications encompassing elliptic PDE's, mixed formulations, first-order PDEs, and the time-dependent versions of these problems. The third part covers implementation issues and should provide readers with most of the practical details needed to write or understand a finite element code. Written at the graduate level, the text contains numerous examples and exercises and is intended to serve as a graduate textbook. Depending on one's interests, several reading paths can be followed, emphasizing either theoretical results, numerical algorithms, code efficiency, or applications in the engineering sciences. The book will be useful to researchers and graduate students in mathematics, computer science and engineering


I Theoretical Foundations -- 1 Finite Element Interpolation -- 2 Approximation in Banach Spaces by Galerkin Methods -- II Approximation of PDEs -- 3 Coercive Problems -- 4 Mixed Problems -- 5 First-Order PDEs -- 6 Time-Dependent Problems -- III Implementation -- 7 Data Structuring and Mesh Generation -- 8 Quadratures, Assembling, and Storage -- 9 Linear Algebra -- 10 A Posteriori Error Estimates and Adaptive Meshes -- IV Appendices -- A Banach and Hilbert Spaces -- A.1 Basic Definitions and Results -- A.2 Bijective Banach Operators -- B Functional Analysis -- B.1 Lebesgue and Lipschitz Spaces -- B.2 Distributions -- B.3 Sobolev Spaces -- Nomenclature -- References -- Author Index

Mathematics Computer science -- Mathematics Mathematical analysis Analysis (Mathematics) Partial differential equations Applied mathematics Engineering mathematics Computer mathematics Mathematics Analysis Applications of Mathematics Math Applications in Computer Science Partial Differential Equations Computational Mathematics and Numerical Analysis Appl.Mathematics/Computational Methods of Engineering


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