Theory and practice of finite elements.
type: Item
instance of: scholarly article
title: Theory and practice of finite elements.
zbMATH Open document ID: 1059.65103
author: Alexandre Ern
author: Jean-Luc Guermond
published in: Applied Mathematical Sciences
publication date: 2004-10-04T00:00:00Z
review text: This book is an expanded version of Lecture Notes published by the authors in French (2002; Zbl 0993.65123). It has been used as a textbook for graduate finite element courses at various French universities and at the University of Texas in Austin. The book can be used in several courses in Mathematics, Computer Science, and Engineering programs. The authors offer suggestions for course titles and syllabi. The book is organized into three parts. The first part (Chapters 1 and 2) reviews the theoretical foundations of the finite element method. The second and third parts are devoted to the practice of finite elements. The second part (Chapters 3 to 6) deals with partial differential equation based applications of finite elements. The third part (Chapters 7 to 10) covers implementation aspects. Two appendices summarize the main mathemaical concepts used in this book: Banach and Hilbert spaces; Banach operators: distributions; and Sobolev spaces. This book is not an exhaustive monograph and always tries to remain at the graduate level. Some aspects of the finite element method are only briefly mentioned or simply alluded to (e.g., the \(p\)- and \(hp\)-versions of the method and the use of hierachical settings). Many bibliographic entries to the extensive literature on finite elements are given throughout the book.
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N50
Mathematics Subject Classification ID: 35A35
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 74S05
Mathematics Subject Classification ID: 76D07
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35K15
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 65-02
Mathematics Subject Classification ID: 76M10
Mathematics Subject Classification ID: 65Y05
Mathematics Subject Classification ID: 65M15
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 78M10
Mathematics Subject Classification ID: 80M10
zbMATH DE Number: 2105694
zbMATH Keywords: finite elements
zbMATH Keywords: textbook
zbMATH Keywords: interpolation
zbMATH Keywords: mixed methods
zbMATH Keywords: error bounds
zbMATH Keywords: incompressible fluids
zbMATH Keywords: Stokes problem
zbMATH Keywords: linear elasticity
zbMATH Keywords: boundary value problems
zbMATH Keywords: Timoshenko beam
zbMATH Keywords: advection-diffusion equation
zbMATH Keywords: algorithms
zbMATH Keywords: Darcy equation
zbMATH Keywords: Maxwell equation
zbMATH Keywords: parabolic problems
zbMATH Keywords: evolution equations
zbMATH Keywords: mesh generation
zbMATH Keywords: iterative methods
zbMATH Keywords: parallel computation
zbMATH Keywords: stability
zbMATH Keywords: numerical examples
reviewed by: I. N. Katz
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2105694