From the reviews: "This book represents an excellent compendium of information about the mathematics and numerical analysis of the finite ... . Its user-ability, for the writing ... is guaranteed through the inclusion of a discussion ... . will be a useful text for advanced mathematics/engineering graduates who wish to learn about ... good background information for the engineer who will eventually apply the finite element method to practical real-world problems. In addition, it will be an excellent text for the mathematics graduate ... . (R.S.Anderssen, Mathematical Reviews, 2005) "This book is an expanded version of Lecture Notes published by the authors in French ... . It has been used as a textbook for graduate finite element courses ... . 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. ... Many bibliographic entries to the extensive literature on finite elements are given throughout the book." (I.N. Katz, Zentralblatt Math, Vol. 1059 (10), 2005) "A relative complete coverage of issues concerning finite element methodology based soundly on theory. ... this is a self-contained presentation which goes relatively far regarding the questions of stability, approximation and error estimation and demonstrates the use of the rather abstract concepts in concrete situations. The presentation is suited for the mathematician and also for applied scientists should they be ready to digest the more abstract concepts which, however, prove very useful understanding how to obtain a working code for the problem at hand." (H. Muthsam, Monatshefte fur Mathematik, Vol. 148 (2), 2006) "Overall, the authors have largery succeeded in giving a rather comprehensive exposition of the finite element method and its challenges, up to some current research topics, in less than 500 pages, yet without taking any unreasonable shortcut, by no means an easy task." (SIAM Review)

• 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.

From the reviews: "This book represents an excellent compendium of information about the mathematics and numerical analysis of the finite ... . Its user-ability, for the writing ... is guaranteed through the inclusion of a discussion ... . will be a useful text for advanced mathematics/engineering graduates who wish to learn about ... good background information for the engineer who will eventually apply the finite element method to practical real-world problems. In addition, it will be an excellent text for the mathematics graduate ... . (R.S.Anderssen, Mathematical Reviews, 2005) "This book is an expanded version of Lecture Notes published by the authors in French ... . It has been used as a textbook for graduate finite element courses ... . 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. ... Many bibliographic entries to the extensive literature on finite elements are given throughout the book." (I.N. Katz, Zentralblatt Math, Vol. 1059 (10), 2005) "A relative complete coverage of issues concerning finite element methodology based soundly on theory. ... this is a self-contained presentation which goes relatively far regarding the questions of stability, approximation and error estimation and demonstrates the use of the rather abstract concepts in concrete situations. The presentation is suited for the mathematician and also for applied scientists should they be ready to digest the more abstract concepts which, however, prove very useful understanding how to obtain a working code for the problem at hand." (H. Muthsam, Monatshefte fur Mathematik, Vol. 148 (2), 2006) "Overall, the authors have largery succeeded in giving a rather comprehensive exposition of the finite element method and its challenges, up to some current research topics, in less than 500 pages, yet without taking any unreasonable shortcut, by no means an easy task." (SIAM Review)

• 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.

From the reviews: "This book represents an excellent compendium of information about the mathematics and numerical analysis of the finite ... . Its user-ability, for the writing ... is guaranteed through the inclusion of a discussion ... . will be a useful text for advanced mathematics/engineering graduates who wish to learn about ... good background information for the engineer who will eventually apply the finite element method to practical real-world problems. In addition, it will be an excellent text for the mathematics graduate ... . (R.S.Anderssen, Mathematical Reviews, 2005) "This book is an expanded version of Lecture Notes published by the authors in French ... . It has been used as a textbook for graduate finite element courses ... . 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. ... Many bibliographic entries to the extensive literature on finite elements are given throughout the book." (I.N. Katz, Zentralblatt Math, Vol. 1059 (10), 2005) "A relative complete coverage of issues concerning finite element methodology based soundly on theory. ... this is a self-contained presentation which goes relatively far regarding the questions of stability, approximation and error estimation and demonstrates the use of the rather abstract concepts in concrete situations. The presentation is suited for the mathematician and also for applied scientists should they be ready to digest the more abstract concepts which, however, prove very useful understanding how to obtain a working code for the problem at hand." (H. Muthsam, Monatshefte fur Mathematik, Vol. 148 (2), 2006) "Overall, the authors have largery succeeded in giving a rather comprehensive exposition of the finite element method and its challenges, up to some current research topics, in less than 500 pages, yet without taking any unreasonable shortcut, by no means an easy task." (SIAM Review)

• 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.