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Numerical Approximation of Partial Differential Equations

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Numerical Approximation of Partial Differential Equations/ by Sören Bartels.
Author:	Bartels, Sören.
Description:	XV, 535 p. 170 illus.online resource. :
Contained By:	Springer Nature eBook
Subject:	Numerical analysis. -
Online resource:	https://doi.org/10.1007/978-3-319-32354-1
ISBN:	9783319323541

Numerical Approximation of Partial Differential Equations
Bartels, Sören.

Numerical Approximation of Partial Differential Equations[electronic resource] /by Sören Bartels. - 1st ed. 2016. - XV, 535 p. 170 illus.online resource. - Texts in Applied Mathematics,640939-2475 ;. - Texts in Applied Mathematics,59.

Preface -- Part I Finite differences and finite elements -- Elliptic partial differential equations -- Finite Element Method -- Part II Local resolution and iterative solution -- Local Resolution Techniques -- Iterative Solution Methods -- Part III Constrained and singularly perturbed problems -- Saddled-point Problems -- Mixed and Nonstandard methods -- Applications -- Problems and Projects -- Implementation aspects -- Notations, inequalities, guidelines -- Index .

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.

ISBN: 9783319323541

Standard No.: 10.1007/978-3-319-32354-1doiSubjects--Topical Terms:

527939
Numerical analysis.

LC Class. No.: QA297-299.4

Dewey Class. No.: 518

Numerical Approximation of Partial Differential Equations
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520 $a 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.
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