The finite element method is a numerical method widely used in engineering. Experience shows that unreliable computation can lead to very serious consequences. Hence reliability questions stand more and more at the forefront of engineering and theoretical interests. The present book presents the mathematical theory of the finite element method and focuses on the question of how reliable computed results really are. It addresses among other topics the local behaviour, errors caused by pollution, superconvergence, and optimal meshes. Many computational examples illustrate the importance of the theoretical conclusions for practical computations. Graduate students, lecturers, and researchers in mathematics, engineering, and scientific computation will benefit from the clear structure of the book, and will find this a very useful reference.

Most of the many books on finite elements are devoted either to mathematical theory or to engineering applications, but not to both. This book seeks to bridge the gap by presenting the main theoretical ideas of the finite element method and the analysis of its errors in an accessible way. At the same time it presents computed numbers which not only illustrate the theory but can only be analysed using the theory. This approach, both dual and interacting between theory and computation makes this book unique. Much research is currently being done into reliability in computational modelling, involving both validation of the mathematical models and verification of the numerical schemes. By treating finite element error analysis in this way this book is a significant contribution to the verification process of finite element modelling in the context of reliability.

The finite element method is a numerical method widely used in engineering. Experience shows that unreliable computation can lead to very serious consequences. Hence reliability questions stand more and more at the forefront of engineering and theoretical interests. The present book presents the mathematical theory of the finite element method and focuses on the question of how reliable computed results really are. It addresses among other topics the local behaviour, errors caused by pollution, superconvergence, and optimal meshes. Many computational examples illustrate the importance of the theoretical conclusions for practical computations. Graduate students, lecturers, and researchers in mathematics, engineering, and scientific computation will benefit from the clear structure of the book, and will find this a very useful reference.

Most of the many books on finite elements are devoted either to mathematical theory or to engineering applications, but not to both. This book seeks to bridge the gap by presenting the main theoretical ideas of the finite element method and the analysis of its errors in an accessible way. At the same time it presents computed numbers which not only illustrate the theory but can only be analysed using the theory. This approach, both dual and interacting between theory and computation makes this book unique. Much research is currently being done into reliability in computational modelling, involving both validation of the mathematical models and verification of the numerical schemes. By treating finite element error analysis in this way this book is a significant contribution to the verification process of finite element modelling in the context of reliability.