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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.