Least-Squares

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Finite Element Methods, Academic/professional/technical: Research and professional
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Finite element methods have become one of the most versatile and powerful methodologies for the approximate numerical solution of PDEs. This book is a thorough yet concise guide to the theory and practice of least-square finite element methods.
This book is written to provide a common, mathematically sound foundation for least-squares finite element methods. It is intended to give both the researcher and the practitioner a concise guide to the theory and practice of least-square finite element methods, their strengths and weaknesses, established successes, and open problems.
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.
Since their emergence, finite element methods have taken a place as one of the most versatile and powerful methodologies for the approximate numerical solution of Partial Differential Equations. These methods are used in incompressible fluid flow, heat, transfer, and other problems. This book provides researchers and practitioners with a concise guide to the theory and practice of least-square finite element methods, their strengths and weaknesses, established successes, and open problems.
Autor: Pavel B. Bochev
ISBN-13:: 9780387308883
ISBN: 0387308881
Erscheinungsjahr: 01.03.2009
Verlag: Springer-Verlag GmbH
Gewicht: 1113g
Seiten: 660
Sprache: Englisch
Sonstiges: Buch, 244x166x43 mm