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Catalogue Information
Field name	Details
Dewey Class	518
Title	Numerical Approximation of Partial Differential Equations ([EBook]) / by Sören Bartels.
Author	Bartels, Sören
Other name(s)	SpringerLink (Online service)
Publication	Cham : : Springer International Publishing : : Imprint: Springer, , 2016.
Physical Details	XV, 535 p. 170 illus. : online resource.
Series	Texts in applied mathematics 0939-2475 ; ; 64
ISBN	9783319323541
Summary Note	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.:
Contents note	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 .
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/10.1007/978-3-319-32354-1
Links to Related Works	Subject References: Mathematics . Numerical Analysis . Partial differential equations . Authors: Bartels, Sören . Corporate Authors: SpringerLink (Online service) . Series: Texts in applied mathematics . Classification: 518 .

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Numerical Approximation of Partial Differential Equations

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