Numerical approximation of partial diffe
β Alfio Quarteroni, Alberto Valli (auth.)
π Library
π
1994
π Springer-Verlag Berlin Heidelberg
π English
β¦ LIBER β¦
π
Numerical Approximation of Partial Differential Equations
β Scribed by SΓΆren Bartels
- Publisher
- Springer
- Year
- 2016
- Tongue
- English
- Leaves
- 541
- Series
- Texts in Applied Mathematics 64
- Edition
- 1st ed.
- Category
- Library
β¬ Acquire This Volume
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β¦ Synopsis
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.Β 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.
β¦ Table of Contents
Front Matter....Pages i-xv
Front Matter....Pages 1-1
Finite Difference Method....Pages 3-64
Elliptic Partial Differential Equations....Pages 65-97
Finite Element Method....Pages 99-152
Front Matter....Pages 153-153
Local Resolution Techniques....Pages 155-207
Iterative Solution Methods....Pages 209-244
Front Matter....Pages 245-245
Saddle-Point Problems....Pages 247-281
Mixed and Nonstandard Methods....Pages 283-347
Applications....Pages 349-404
Back Matter....Pages 405-535
β¦ Subjects
Mathematics;Partial differential equations;Numerical analysis;Numerical Analysis;Partial Differential Equations
π SIMILAR VOLUMES
Numerical approximation of partial diffe
β Alfio Quarteroni, Alberto Valli (auth.)
π Library
π
1994
π Springer-Verlag Berlin Heidelberg
π English
<p><P>This book deals with the numerical approximation of partial differential equations. Its scope is to provide a thorough illustration of numerical methods, carry out their stability and convergence analysis, derive error bounds, and discuss the algorithmic aspects relative to their implementatio
Numerical Approximation of Partial Diffe
β SΓΆren Bartels (auth.)
π Library
π
2016
π Springer International Publishing
π English
<p>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 meth
Partial Differential Equations: Modeling
β HervΓΒ© Le Dret, Brigitte Lucquin
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2016
π BirkhΓΒ€user
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Partial Differential Equations: Modeling
β HervΓ© Le Dret, Brigitte Lucquin (auth.)
π Library
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2016
π BirkhΓ€user Basel
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<p><p>This book is devoted to the study of partial differential equation problems both from the theoretical and numerical points of view. After presenting modeling aspects, it develops the theoretical analysis of partial differential equation problems for the three main classes of partial differenti
Numerical Approximation of Partial Diffe
β Eduardo L. Ortiz (editor)
π Library
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1987
π Elsevier Science Ltd
π English
<span>This selection of papers is concerned with problems arising in the numerical solution of differential equations, with an emphasis on partial differential equations. There is a balance between theoretical studies of approximation processes, the analysis of specific numerical techniques and the