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Elliptic eifferential equationstheor...

Hackbusch, Wolfgang.

Elliptic eifferential equationstheory and numerical treatment /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Elliptic eifferential equationsby Wolfgang Hackbusch.
其他題名:	theory and numerical treatment /
作者:	Hackbusch, Wolfgang.
出版者:	Berlin, Heidelberg :Springer Berlin Heidelberg :2017.
面頁冊數:	xiv, 455 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer eBooks
標題:	Differential equations, Elliptic.
電子資源:	http://dx.doi.org/10.1007/978-3-662-54961-2
ISBN:	9783662549612$q(electronic bk.)

Elliptic eifferential equationstheory and numerical treatment /
Hackbusch, Wolfgang.

Elliptic eifferential equationstheory and numerical treatment /[electronic resource] :by Wolfgang Hackbusch. - 2nd ed. - Berlin, Heidelberg :Springer Berlin Heidelberg :2017. - xiv, 455 p. :ill. (some col.), digital ;24 cm. - Springer series in computational mathematics,180179-3632 ;. - Springer series in computational mathematics ;42..

1 Partial Differential Equations and Their Classification Into Types -- 2 The Potential Equation -- 3 The Poisson Equation -- 4 Difference Methods for the Poisson Equation -- 5 General Boundary Value Problems -- 6 Tools from Functional Analysis -- 7 Variational Formulation -- 8 The Method of Finite Elements -- 9 Regularity -- 10 Special Differential Equations -- 11 Eigenvalue Problems -- 12 Stokes Equations.

This book simultaneously presents the theory and the numerical treatment of elliptic boundary value problems, since an understanding of the theory is necessary for the numerical analysis of the discretisation. It first discusses the Laplace equation and its finite difference discretisation before addressing the general linear differential equation of second order. The variational formulation together with the necessary background from functional analysis provides the basis for the Galerkin and finite-element methods, which are explored in detail. A more advanced chapter leads the reader to the theory of regularity. Individual chapters are devoted to singularly perturbed as well as to elliptic eigenvalue problems. The book also presents the Stokes problem and its discretisation as an example of a saddle-point problem taking into account its relevance to applications in fluid dynamics.

ISBN: 9783662549612$q(electronic bk.)

Standard No.: 10.1007/978-3-662-54961-2doiSubjects--Topical Terms:

205654
Differential equations, Elliptic.

LC Class. No.: QA377

Dewey Class. No.: 515.3533

Elliptic eifferential equationstheory and numerical treatment /
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520 $a This book simultaneously presents the theory and the numerical treatment of elliptic boundary value problems, since an understanding of the theory is necessary for the numerical analysis of the discretisation. It first discusses the Laplace equation and its finite difference discretisation before addressing the general linear differential equation of second order. The variational formulation together with the necessary background from functional analysis provides the basis for the Galerkin and finite-element methods, which are explored in detail. A more advanced chapter leads the reader to the theory of regularity. Individual chapters are devoted to singularly perturbed as well as to elliptic eigenvalue problems. The book also presents the Stokes problem and its discretisation as an example of a saddle-point problem taking into account its relevance to applications in fluid dynamics.
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