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Field name	Details
Dewey Class	511.42
Title	Least-Squares Finite Element Methods ([Ebook]) / by Max D. Gunzburger, Pavel B. Bochev.
Author	Gunzburger, Max D.
Added Personal Name	Bochev, Pavel B.
Other name(s)	SpringerLink (Online service)
Publication	New York, NY : Springer , 2009.
Physical Details	XXII, 660 pages : online resource.
Series	Applied mathematical sciences 0066-5452 ; ; 166
ISBN	9780387689227
Summary Note	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.:
Contents note	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.
System details note	Online Access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/b13382
Links to Related Works	Subject References: Calculus of variations and optimal control; optimization . Computational Mathematics and Numerical Analysis . Computer Science . Engineering Fluid Dynamics . Hydraulic engineering . Mathematical optimization . Mathematics . Authors: author . Bochev, Pavel B. . Gunzburger, Max D. . Corporate Authors: SpringerLink (Online service) . Series: Applied mathematical sciences . Classification: 511.42 . 511.42 (DDC 23) .

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Least-Squares Finite Element Methods

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