Numerical Approximation of Partial Differential Equations (Hardcover)

Soeren Bartels

ISBN 10: 3319323539 / ISBN 13: 9783319323534

Verlag: Springer International Publishing AG, Cham, 2016

Beschreibung

Hardcover. Finite element methods for approximating partial differential equations have reached a high degree of maturity, and are an indispensible tool in science and technology. This textbook aims at providing a thorough introduction to the construction, analysis, and implementation of finite element methods for model problems arising in continuum mechanics. The first part of the book discusses elementary properties of linear partial differential equations along with their basic numerical approximation, the functional-analytical framework for rigorously establishing existence of solutions, and the construction and analysis of basic finite element methods. The second part is devoted to the optimal adaptive approximation of singularities and the fast iterative solution of linear systems of equations arising from finite element discretizations. In the third part, the mathematical framework for analyzing and discretizing saddle-point problems is formulated, corresponding finte element methods are analyzed, and particular applications including incompressible elasticity, thin elastic objects, electromagnetism, and fluid mechanics are addressed. The book includes theoretical problems and practical projects for all chapters, and an introduction to the implementation of finite element methods. Finite element methods for approximating partial differential equations have reached a high degree of maturity, and are an indispensible tool in science and technology. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Bestandsnummer des Verkäufers 9783319323534

Bibliografische Details

• Titel: Numerical Approximation of Partial Differential Equations (Hardcover)
• Verlag: Springer International Publishing AG, Cham
• Erscheinungsjahr: 2016
• Sprache: Englisch
• ISBN-10: 3319323539
• ISBN-13: 9783319323534
• Einband: Hardcover
• Auflage: 1. Auflage
• Zustand: new

Über diesen Titel

Inhaltsangabe

Finite element methods for approximating partial differential equations have reached a high degree of maturity, and are an indispensible tool in science and technology. This textbook aims at providing a thorough introduction to the construction, analysis, and implementation of finite element methods for model problems arising in continuum mechanics. The first part of the book discusses elementary properties of linear partial differential equations along with their basic numerical approximation, the functional-analytical framework for rigorously establishing existence of solutions, and the construction and analysis of basic finite element methods. The second part is devoted to the optimal adaptive approximation of singularities and the fast iterative solution of linear systems of equations arising from finite element discretizations. In the third part, the mathematical framework for analyzing and discretizing saddle-point problems is formulated, corresponding finte element methods are analyzed, and particular applications including incompressible elasticity, thin elastic objects, electromagnetism, and fluid mechanics are addressed. The book includes theoretical problems and practical projects for all chapters, and an introduction to the implementation of finite element methods.

Über die Autorin bzw. den Autor

Sören Bartels is Professor of Applied Mathematics at the Albert-Ludwigs University in Freiburg, Germany. His primary research interest is in the development and analysis of approximation schemes for nonlinear partial differential equations with applications in the simulation of modern materials. Professor Bartels has published the Springer textbook "Numerik 3x9" and the monograph "Numerical methods for nonlinear partial differential equations" in the Springer Series in Computational Mathematics.