Overview
The description of many interesting phenomena in science and engineering leads to infinite-dimensional minimization or evolution problems that define nonlinear partial differential equations. While the development and analysis of numerical methods for linear partial differential equations is nearly complete, only few results are available in the case of nonlinear equations. This monograph devises numerical methods for nonlinear model problems arising in the mathematical description of phase transitions, large bending problems, image processing, and inelastic material behavior. For each of these problems the underlying mathematical model is discussed, the essential analytical properties are explained, and the proposed numerical method is rigorously analyzed. The practicality of the algorithms is illustrated by means of short implementations.
Full Product Details
Author: Sören Bartels
Publisher: Springer International Publishing AG
Imprint: Springer International Publishing AG
Edition: Softcover reprint of the original 1st ed. 2015
Volume: 47
Dimensions:
Width: 15.50cm
, Height: 2.10cm
, Length: 23.50cm
Weight: 6.088kg
ISBN: 9783319356808
ISBN 10: 3319356801
Pages: 393
Publication Date: 22 October 2016
Audience:
Professional and scholarly
,
Professional & Vocational
Format: Paperback
Publisher's Status: Active
Availability: Manufactured on demand
We will order this item for you from a manufactured on demand supplier.
Reviews
This book presents an ambitious overview of modern results and trends in the field of numerical methods for nonlinear PDEs, with an emphasis on the finite element method. ... The target audience of the book is postgraduates and experienced researchers. ... this is an excellent monograph describing methods found at the intersection of numerical PDEs and the calculus of variations. (Michael Neilan, SIAM Review, Vol. 58 (3), September, 2016) This book provides advanced students and experimental researchers with an introduction to numerical methods for nonlinear partial differential equations, in particular those originating from continuum mechanics. ... This book presents a very nice transition from graduate-level material to state-of-the-art research topics. ... This is a nice and well-written advanced textbook. (Karsten Urban, Mathematical Reviews, October, 2015)
This book presents an ambitious overview of modern results and trends in the field of numerical methods for nonlinear PDEs, with an emphasis on the finite element method. ... The target audience of the book is postgraduates and experienced researchers. ... this is an excellent monograph describing methods found at the intersection of numerical PDEs and the calculus of variations. (Michael Neilan, SIAM Review, Vol. 58 (3), September, 2016) This book provides advanced students and experimental researchers with an introduction to numerical methods for nonlinear partial differential equations, in particular those originating from continuum mechanics. ... This book presents a very nice transition from graduate-level material to state-of-the-art research topics. ... This is a nice and well-written advanced textbook. (Karsten Urban, Mathematical Reviews, October, 2015)
“This book presents an ambitious overview of modern results and trends in the field of numerical methods for nonlinear PDEs, with an emphasis on the finite element method. … The target audience of the book is postgraduates and experienced researchers. … this is an excellent monograph describing methods found at the intersection of numerical PDEs and the calculus of variations.” (Michael Neilan, SIAM Review, Vol. 58 (3), September, 2016) “This book provides advanced students and experimental researchers with an introduction to numerical methods for nonlinear partial differential equations, in particular those originating from continuum mechanics. … This book presents a very nice transition from graduate-level material to state-of-the-art research topics. … This is a nice and well-written advanced textbook.” (Karsten Urban, Mathematical Reviews, October, 2015)
This book provides advanced students and experimental researchers with an introduction to numerical methods for nonlinear partial differential equations, in particular those originating from continuum mechanics. This book presents a very nice transition from graduate-level material to state-of-the-art research topics. This is a nice and well-written advanced textbook. (Karsten Urban, Mathematical Reviews, October, 2015)
