A Posteriori Error Estimation Techniques for Finite Element Methods

Hardcover | July 6, 2013

byRudiger Verfurth

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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 maintools 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 commonprinciples. 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.

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From the Publisher

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 maintools in achieving this goal are a posterior...

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 Me...
Format:HardcoverDimensions:416 pages, 9.21 × 6.14 × 0.98 inPublished:July 6, 2013Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0199679428

ISBN - 13:9780199679423

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Table of Contents

1. A Simple Model Problem2. Implementation3. Auxiliary Results4. Linear Elliptic Equations5. Nonlinear Elliptic Equations6. Parabolic Equations

Editorial Reviews

"Error control and adaptive solution algorithms for finite element approximation are a key concern of every practitioner. The present text, written by a leading authority in the field who has made many important contributions, will be valuable for theoreticians and practitioners alike." --Mark Ainsworth, Professor of Applied Mathematics, Brown University