Quality Assurance and Tolerance

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Alexandre Ern, Jean-Luc Guermond

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.

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A. Halanay, V. Răsvan

This volume, which coincides with the centennial anniversary of the publication of the celebrated monograph The General Problem of the Stability Motion by A.M. Liapunov, reviews the current state of the art of the theory and applications of the Liapunov methods. The book contains an Introduction and four chapters. Chapter 2 presents some general results in stability theory. The remaining chapters deal with applications in power engineering, chemical engineering, and in non-engineering fields such as economics and in the modelling of interacting species. The beauty of the results obtained, the diversity of mathematical tools employed, and the described approach to mathematical modelling provide stimulating considerations for applications in many other fields. For mathematicians and engineers whose work involves the study and applications of stability theory in systems.

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Yu. A. Mitropolskii, Nguyen Dao

The present volume addresses the application of asymptotic methods in nonlinear oscillations. Such methods see a large variety of applications in physics, mechanics and engineering. The advantages of using asymptotic methods in solving nonlinear problems are firstly simplicity, especially for computing higher approximations, and secondly their applicability to a large class of quasi-linear systems. In contrast to the existing literature, this book is concerned with the applied aspects of the methods concerned and also contains problems relevant to the everyday practice of engineers, physicists and mathematicians. Usually, dynamics systems are classified and examined by their degrees of freedom. This book is constructed from another point of view based upon the originating mechanism of the oscillations: free oscillation, self-excited oscillation, forced oscillation, and parametrically excited oscillation. The text has been designed to cover material from the elementary to the more advanced, in increasing order of difficulty. It is of considerable interest to both students and researchers in applied mathematics, physical and mechanical sciences, and engineering.

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Victor Gutenmacher, N.B. Vasilyev

"This newly revised and expanded edition includes more than 200 theoretical and practical problems in which formal geometry provides simple and elegant insight, and the book points the reader toward important areas of modern mathematics." "Lines and Curves is well positioned for companion use with software packages like The Geometer's Sketchpad, and it can serve as a guidebook for engineers. Its deeper, interdisciplinary treatment is ideal for more theoretical readers, and the development from first principles makes the book accessible to undergraduates, advanced high school students, teachers, and puzzle enthusiasts alike."--BOOK JACKET.