John Whiteman

Theofanis Strouboulis

Ivo Babuska

Computational modelling is the process of representing some activity, for example a physical happening, first by a mathematical model and then of solving the model using a numerical technique such as the finite element method. Both parts of this process involve approximations. As a result error estimation has to be employed to assess the reliability of the computational modelling process. This book addresses the verification of the numerical methods, in thiscase finite elements methods, involved in the process, by analysing the finite element errors. The unique feature of the book is that it brings together both theoretical error analysis and the computed solutions, highlighting their interplay.

An Introduction to the Method and Error Estimation

Finite Elements

Ivo Babus̆ka, Theofanis Strouboulis

Ivo Babuška

John Robert Whiteman

Professor of Aerospace Engineering and Engineering Science and Professor of Mathematics Ivo Babuska

Associate Professor Department of Aerospace Engineering Theofanis Strouboulis

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 are at the forefront of engineering and theoretical interests. This book presents the mathematical theory of the finite element method and is the first to focus on the questions 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.

The Finite Element Method and Its Reliability

Theofanis Strouboulis

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