Pavel B. Bochev, Max D. Gunzburger

Least-Squares Finite Element Methods (eBook, PDF)

• Format: PDF

Produktbeschreibung

The book examines theoretical and computational aspects of least-squares finite element methods(LSFEMs) for partial differential equations (PDEs) arising in key science and engineering applications. It is intended for mathematicians, scientists, and engineers interested in either or both the theory and practice associated with the numerical solution of PDEs. The first part looks at strengths and weaknesses of classical variational principles, reviews alternative variational formulations, and offers a glimpse at the main concepts that enter into the formulation of LSFEMs. Subsequent parts introduce mathematical frameworks for LSFEMs and their analysis, apply the frameworks to concrete PDEs, and discuss computational properties of resulting LSFEMs. Also included are recent advances such as compatible LSFEMs, negative-norm LSFEMs, and LSFEMs for optimal control and design problems. Numerical examples illustrate key aspects of the theory ranging from the importance of norm-equivalence to connections between compatible LSFEMs and classical-Galerkin and mixed-Galerkin methods. Pavel Bochev is a Distinguished Member of the Technical Staff at Sandia National Laboratories with research interests in compatible discretizations for PDEs, multiphysics problems, and scientific computing. Max Gunzburger is Frances Eppes Professor of Scientific Computing and Mathematics at Florida State University and recipient of the W.T. and Idelia Reid Prize in Mathematics from the Society for Industrial and Applied Mathematics.

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Produktdetails

• Verlag: Springer US
• Seitenzahl: 660
• Erscheinungstermin: 28. April 2009
• Englisch
• ISBN-13: 9780387689227
• Artikelnr.: 37286210

Inhaltsangabe

Part I. Survey of Variational Principles and Associated Finite Element Methods. Classical Variational Methods. Alternative Variational Formulations.- Part II. Abstract Theory of Least-Squares Finite Element Methods. Mathematical Foundations. First-Order Agmon-Douglis-Nirenberg Systems.- Part III. Least-Squares Methods for Elliptic Problems. Basic First-Order Systems. Application to Key Elliptic Problems.- Part IV. Extensions of Least-Squares Methods to other Problems. The Navier-Stokes Equations. Dissipative Time Dependent Problems. Hyperbolic Problems. Control and optimization Problems. Other Topics.- Part V. Supplementary Material.- A. Analysis Tools. B. Finite Element Spaces. C. Discrete Norms and Operators. D. The Complementing Condition.

Rezensionen

From the reviews: "In the book under review, the authors give a unified and comprehensive treatment of least-squares finite element methods and discuss important implementation issues that are critical to their success in practice. ... This book is valuable both for researchers and practitioners working in least-squares finite element methods. ... In addition, others will find it a great reference for learning about the theory and implementation of the least-squares finite element methods." (Tsu-Fen Chen, Mathematical Reviews, Issue 2010 b)