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Numerical Approximation of Partial Differential Equations

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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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Detail Information

Series Title

Texts in Applied Mathematics

Call Number

-

Publisher

Cham, Switzerland : Springer., 2016

Collation

XV, 535

Language

English

ISBN/ISSN

978-3-319-32353-4

Classification

NONE

Content Type

text

Media Type

computer

Carrier Type

online resource

Edition

1

Subject(s)

Numerical Analysis
Differential equations

Specific Detail Info

-

Statement of Responsibility

Sören Bartels

Other Information

Cataloger

Devi

Source

-

Validator

Taufik

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