A Posteriori Error Analysis Via Duality Theory: With Applications in Modeling and Numerical Approximations

ISBN-13: 9781441936363 / Angielski / Miękka / 2010 / 302 str.

Weimin Han

Opis

This volume provides a posteriori error analysis for mathematical idealizations in modeling boundary value problems, especially those arising in mechanical applications, and for numerical approximations of numerous nonlinear variational problems. The author avoids giving the results in the most general, abstract form so that it is easier for the reader to understand more clearly the essential ideas involved. Many examples are included to show the usefulness of the derived error estimates.

Recenzje

From the reviews:

"The subject of this book is the a posterior error analysis for mathematical idealizations in applied boundary value problems (BVPs) ... . A very nice book, well structured and written, coupling mathematical theory and numerical results and tests for applied problems." (Viorel Arnautu, Zentralblatt MATH, Vol. 1081, 2006)

"I believe that this book is the first book to present a systematical study in applying the duality theory to deriving a posteriori error estimates for a variety of interesting problems. ... The book is very well written. ... this nice book is quite easy to follow. I believe that the book will be very useful for researchers and graduate students in applied and computational mathematics and engineering." (Wen Bin Liu, Mathematical Reviews, Issue 2005 k)

Spis treści

Preliminaries.- Elements of Convex Analysis, Duality Theory.- A Posteriori Error Analysis for Idealizations in Linear Problems.- A Posteriori Error Analysis for Linearizations.- A Posteriori Error Analysis for Some Numerical Procedures.- Error Analysis for Variational Inequalities of the Second Kind.

Blurb

This volume provides a posteriori error analysis for mathematical idealizations in modeling boundary value problems, especially those arising in mechanical applications, and for numerical approximations of numerous nonlinear variational problems. The author avoids giving the results in the most general, abstract form so that it is easier for the reader to understand more clearly the essential ideas involved. Many examples are included to show the usefulness of the derived error estimates.

Audience

This volume is suitable for researchers and graduate students in applied and computational mathematics, and in engineering.