A Posteriori Error Estimation Techniques for Finite Element Methods (Hardcover)

Ruediger Verfuerth

ISBN 10: 0199679428 / ISBN 13: 9780199679423

Published by Oxford University Press, Oxford, 2013

About this Item

Hardcover. Self-adaptive discretization methods are now an indispensable tool for the numerical solution of partial differential equations that arise from physical and technical applications. The aim is to obtain a numerical solution within a prescribed tolerance using a minimal amount of work. The main tools in achieving this goal are a posteriori error estimates which give global and local information on the error of the numerical solution and which can easily be computedfrom the given numerical solution and the data of the differential equation. This book reviews the most frequently used a posteriori error estimation techniques and applies them toa broad class of linear and nonlinear elliptic and parabolic equations. Although there are various approaches to adaptivity and a posteriori error estimation, they are all based on a few common principles. The main aim of the book is to elaborate these basic principles and to give guidelines for developing adaptive schemes for new problems. Chapters 1 and 2 are quite elementary and present various error indicators and their use for mesh adaptation in the framework of asimple model problem. The basic principles are introduced using a minimal amount of notations and techniques providing a complete overview for the non-specialist. Chapters 4-6 on the other hand are moreadvanced and present a posteriori error estimates within a general framework using the technical tools collected in Chapter 3. Most sections close with a bibliographical remark which indicates the historical development and hints at further results. A posteriori error estimation techniques are fundamental to the efficient numerical solution of PDEs arising in physical and technical applications. This book gives a unified approach to these techniques and guides graduate students, researchers, and practitioners towards understanding, applying and developing self-adaptive discretization methods. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Seller Inventory # 9780199679423

Bibliographic Details

• Title: A Posteriori Error Estimation Techniques for Finite Element Methods (Hardcover)
• Publisher: Oxford University Press, Oxford
• Publication Date: 2013
• Language: English
• ISBN 10: 0199679428
• ISBN 13: 9780199679423
• Binding: Hardcover
• Condition: new

About this title

Synopsis

Self-adaptive discretization methods are now an indispensable tool for the numerical solution of partial differential equations that arise from physical and technical applications. The aim is to obtain a numerical solution within a prescribed tolerance using a minimal amount of work. The main tools in achieving this goal are a posteriori error estimates which give global and local information on the error of the numerical solution and which can easily be computed from the given numerical solution and the data of the differential equation.

This book reviews the most frequently used a posteriori error estimation techniques and applies them to a broad class of linear and nonlinear elliptic and parabolic equations. Although there are various approaches to adaptivity and a posteriori error estimation, they are all based on a few common principles. The main aim of the book is to elaborate these basic principles and to give guidelines for developing adaptive schemes for new problems.

Chapters 1 and 2 are quite elementary and present various error indicators and their use for mesh adaptation in the framework of a simple model problem. The basic principles are introduced using a minimal amount of notations and techniques providing a complete overview for the non-specialist. Chapters 4-6 on the other hand are more advanced and present a posteriori error estimates within a general framework using the technical tools collected in Chapter 3. Most sections close with a bibliographical remark which indicates the historical development and hints at further results.

About the Author

Rudiger Verfurth is Chair for Numerical Analysis at Ruhr-University, Bochum. He is a renowned expert in a posteriori error estimation and has been the Associate Editor of the SIAM Journal on Numerical Analysis since 2001. He has previously written a well-known book in the area: A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques (Wiley, 1996)