The first investigations of nonlinear approximation problems were made by P.L. Chebyshev in the last century, and the entire theory of uniform approxima­ tion is strongly connected with his name. By making use of his ideas, the theories of best uniform approximation by rational functions and by polynomials were developed over the years in an almost unified framework. The difference between linear and rational approximation and its implications first became apparent in the 1960's. At roughly the same time other approaches to nonlinear approximation were also developed. The use of new tools, such as nonlinear functional analysis and topological methods, showed that linearization is not sufficient for a complete treatment of nonlinear families. In particular, the application of global analysis and the consideration of flows on the family of approximating functions intro­ duced ideas which were previously unknown in approximation theory. These were and still are important in many branches of analysis. On the other hand, methods developed for nonlinear approximation prob­ lems can often be successfully applied to problems which belong to or arise from linear approximation. An important example is the solution of moment problems via rational approximation. Best quadrature formulae or the search for best linear spaces often leads to the consideration of spline functions with free nodes. The most famous problem of this kind, namely best interpolation by poly­ nomials, is treated in the appendix of this book.

Nonlinear Approximation Theory (SPRINGER SERIES IN COMPUTATIONAL MATHEMATICS)

Science & Math

Braess, Dietrich

Mathematics

Springer, Verlag

Sharing the Difference: Feminist Debates in Holland

Finite Elements: Theory, Fast Solvers, and Applications in Solid Mechanics

Cambridge University Press

This definitive introduction to finite element methods was thoroughly updated for this 2007 third edition, which features important material for both research and application of the finite element method. The discussion of saddle-point problems is a highlight of the book and has been elaborated to include many more nonstandard applications. The chapter on applications in elasticity now contains a complete discussion of locking phenomena. The numerical solution of elliptic partial differential equations is an important application of finite elements and the author discusses this subject comprehensively. These equations are treated as variational problems for which the Sobolev spaces are the right framework. Graduate students who do not necessarily have any particular background in differential equations, but require an introduction to finite element methods will find this text invaluable. Specifically, the chapter on finite elements in solid mechanics provides a bridge between mathematics and engineering.

In this thoroughly revised version of the successful first edition, the author has added new material that will prove useful for research or application of the finite element method. The most important application of finite elements is the numerical solution of elliptic partial differential equations. The author provides thorough coverage of this subject and includes aspects such as saddle point problems that require a more in-depth mathematical treatment.

Reference

Foreign Language Study & Reference

The most important application of the finite element method is the numerical solution of elliptical partial differential equations. This is covered in depth in this book. It is a textbook for graduate students who do not necessarily have any particular background in differential equations, but require an introduction to finite elements for engineering or mathematics applications.

This definitive introduction to finite element methods was thoroughly updated for this 2007 third edition, which features important material for both research and application of the finite element method. The discussion of saddle-point problems is a highlight of the book and has been elaborated to include many more nonstandard applications. The chapter on applications in elasticity now contains a complete discussion of locking phenomena. The numerical solution of elliptic partial differential equations is an important application of finite elements and the author discusses this subject comprehensively. These equations are treated as variational problems for which the Sobolev spaces are the right framework. Graduate students who do not necessarily have any particular background in differential equations, but require an introduction to finite element methods will find this text invaluable. Specifically, the chapter on finite elements in solid mechanics provides a bridge between mathematics and engineering.

Includes chapters on humane caring for the renal patient--addressing chronic illness, narrative ethics, advance directives, and terminal care--and on the role of nurses in caring for the renal patient. The 3rd edition provides additional relevant clinical examples through numerous case studies, but retains the boxes, tables, and bolding that make the book an excellent, concise and accessible reference resource.
<li>Delivers fully updated coverage throughout, including 2 new chapters on Humane Caring for the Renal Patient, Chronic Illness, Narrative Ethics, Advance Directives, and Terminal Care and The Role of the Nurse in Caring for the Renal Patient.</li>Offers a more patient-focused, clinical orientation and more case studies. Examines the specific problems of approximately 50 patients with renal disease, highlighting preferred diagnosis and management approaches and follow-up measures. <li>Provides a stronger primary care/family practice focus--addressing the needs of physicians, nurses, physician assistants, and more, including information on consulting a nephrologist.</li>OUTSTANDING FEATURES: <li>Captures the insights of the foremost authorities in the field. </li>Equips readers with rationales for specific treatment recommendations.<li>Presents comprehensive drug tables that provide a quick bedside reference to the latest drugs and dosages.</li>

During the week of December 8-13, 1984, a conference on Multi-Grid Methods was held at the Mathematisches Forschungs- institut (Mathematical Research Institute) in Oberwolfach. The conference was suggested by the GAMM-Committee "Effiziente numerische Verfahren fUr partielle Differentialgleichungen." We were pleased to have 42 participants from 12 countries. These proceedings contain some contributions to the confe- rence. The centre of interest in the more theoretical contri- butions were exact convergence proofs for multi-grid method. Here, the theoretical foundation for the application of the method to the Stokes equations, the biharmonic equation in its formulation as a mixed finite element problem and other more involved problems were investigated. Moreover, improvements and new attacks for getting quantitative results on convergence rates were reported. Another series of contributions was concerned with the de- velopment of highly efficient and fast algorithms for various partial differential equations. Also in this framework, the Stokes and the biharmonic equations were investigated. Other lectures treated problems from fluid mechanics (as Navier- Stokes and Euler equations), the dam-problem and eigenvalue problems. The editors would like to thank Professor M. Barner, the director of Mathematisches Forschungsinstitut Oberwolfach for making this conference possible. D. Braess, Bochum W. Hackbusch, Kiel U. Trottenberg, St. Augustin v CONTENTS O. AXELSSON: A mixed variable finite element method for the efficient solution of nonlinear diffusion and pot- tial flow equations ................................... .

Advances in Multi-Grid Methods: Proceedings of the conference held in Oberwolfach, December 8 to 13, 1984 (Notes on Numerical Fluid Mechanics and Multidisciplinary Design, 11) (German Edition)

Trottenberg, Ulrich

Hackbusch, Wolfgang

Vieweg+Teubner Verlag

Bei der numerischen Behandlung partieller Differentialgleichungen treten oft überraschende Phänomene auf. Neben der zügigen Behandlung der klassischen Theorie, die bis an die aktuelle Forschung heranführt, wird deshalb viel Wert auf die Darstellung von Beispielen und Gegenbeispielen gelegt. Die Beispiele haben mit dazu beigetragen, dass das Buch jetzt zu den Standardwerken bei den Finiten Elementen zählt.Mit der fünften Auflage erfolgte eine weitere Abrundung bei den Themen, deren Bedeutung  in den letzten Jahren gewachsen ist. Mit der Theorie der a posteriori Fehlerschätzer wird  a priori Information über den Diskretisierungsfehler  gewonnen, die in der klassischen Theorie noch nicht hergeleitet wurden und die – schärfer als sonst –eine Eigenart von a posteriori Schätzern beleuchtet. Die Behandlung von Platten in der Festkörpermechanik erhält jetzt mit dem Zwei-Energien-Prinzip eine solide Grundlage, nachdem in der letzten Auflage die Behandlung von Locking Effekten in eine vollständige Theorie mündete.Das Buch richtet sich an Studierende der Mathematik im 3. Und 4. Studienjahr und in den späteren Kapiteln auch an junge Forscher, bei denen Finite Elemente im Mittelpunkt ihrer Arbeit stehen.

Finite Elemente: Theorie, schnelle Löser und Anwendungen in der Elastizitätstheorie (Masterclass) (German Edition)

Springer Spektrum

See the best price to sell, buy, or rent books by Braess, Dietrich. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Braess, Dietrich

See the best price to sell, buy, or rent books by Braess, Dietrich. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Nonlinear Approximation Theory (SPRINGER SERIES IN COMPUTATIONAL MATHEMATICS)

Finite Elements: Theory, Fast Solvers, and Applications in Solid Mechanics

Finite Elements: Theory, Fast Solvers, and Applications in Solid Mechanics

Finite Elements: Theory, Fast Solvers, and Applications in Solid Mechanics

Finite Elements: Theory, Fast Solvers, and Applications in Solid Mechanics

Finite Elements: Theory, Fast Solvers, and Applications in Solid Mechanics

Finite Elements: Theory, Fast Solvers, and Applications in Solid Mechanics

Finite Elements: Theory, Fast Solvers, and Applications in Solid Mechanics

Advances in Multi-Grid Methods: Proceedings of the conference held in Oberwolfach, December 8 to 13, 1984 (Notes on Numerical Fluid Mechanics and Multidisciplinary Design, 11) (German Edition)

Finite Elemente: Theorie, schnelle Löser und Anwendungen in der Elastizitätstheorie (Masterclass) (German Edition)