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010   $a3-662-54961-1
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101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aElliptic Differential Equations $eTheory and Numerical Treatment /$fby Wolfgang Hackbusch
205   $a2nd ed. 2017.
210  1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2017.
215   $a1 online resource (XIV, 455 p. 55 illus., 15 illus. in color.) 
225 1 $aSpringer Series in Computational Mathematics,$x0179-3632 ;$v18
311   $a3-662-54960-3 
320   $aIncludes bibliographical references and index.
327   $a1 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.
330   $aThis book simultaneously presents the theory and the numerical treatment of elliptic boundary value problems, since an understanding of the theory is necessary for the numerical analysis of the discretisation. It first discusses the Laplace equation and its finite difference discretisation before addressing the general linear differential equation of second order. The variational formulation together with the necessary background from functional analysis provides the basis for the Galerkin and finite-element methods, which are explored in detail. A more advanced chapter leads the reader to the theory of regularity. Individual chapters are devoted to singularly perturbed as well as to elliptic eigenvalue problems. The book also presents the Stokes problem and its discretisation as an example of a saddle-point problem taking into account its relevance to applications in fluid dynamics.
410  0$aSpringer Series in Computational Mathematics,$x0179-3632 ;$v18
606   $aMathematical analysis
606   $aAnalysis (Mathematics)
606   $aNumerical analysis
606   $aSystem theory
606   $aCalculus of variations
606   $aMathematical physics
606   $aAnalysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12007
606   $aNumerical Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M14050
606   $aSystems Theory, Control$3https://scigraph.springernature.com/ontologies/product-market-codes/M13070
606   $aCalculus of Variations and Optimal Control; Optimization$3https://scigraph.springernature.com/ontologies/product-market-codes/M26016
606   $aTheoretical, Mathematical and Computational Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/P19005
615  0$aMathematical analysis.
615  0$aAnalysis (Mathematics).
615  0$aNumerical analysis.
615  0$aSystem theory.
615  0$aCalculus of variations.
615  0$aMathematical physics.
615 14$aAnalysis.
615 24$aNumerical Analysis.
615 24$aSystems Theory, Control.
615 24$aCalculus of Variations and Optimal Control; Optimization.
615 24$aTheoretical, Mathematical and Computational Physics.
676   $a515.353
700   $aHackbusch$b Wolfgang$4aut$4http://id.loc.gov/vocabulary/relators/aut$051792
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910254284203321
996   $aElliptic differential equations$9382567
997   $aUNINA