04064nam 22006975 450 991025428420332120200629145517.03-662-54961-110.1007/978-3-662-54961-2(CKB)3710000001393639(DE-He213)978-3-662-54961-2(MiAaPQ)EBC4871096(PPN)202987973(EXLCZ)99371000000139363920170602d2017 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierElliptic Differential Equations Theory and Numerical Treatment /by Wolfgang Hackbusch2nd ed. 2017.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2017.1 online resource (XIV, 455 p. 55 illus., 15 illus. in color.) Springer Series in Computational Mathematics,0179-3632 ;183-662-54960-3 Includes bibliographical references and index.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.Springer Series in Computational Mathematics,0179-3632 ;18Mathematical analysisAnalysis (Mathematics)Numerical analysisSystem theoryCalculus of variationsMathematical physicsAnalysishttps://scigraph.springernature.com/ontologies/product-market-codes/M12007Numerical Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M14050Systems Theory, Controlhttps://scigraph.springernature.com/ontologies/product-market-codes/M13070Calculus of Variations and Optimal Control; Optimizationhttps://scigraph.springernature.com/ontologies/product-market-codes/M26016Theoretical, Mathematical and Computational Physicshttps://scigraph.springernature.com/ontologies/product-market-codes/P19005Mathematical analysis.Analysis (Mathematics).Numerical analysis.System theory.Calculus of variations.Mathematical physics.Analysis.Numerical Analysis.Systems Theory, Control.Calculus of Variations and Optimal Control; Optimization.Theoretical, Mathematical and Computational Physics.515.353Hackbusch Wolfgangauthttp://id.loc.gov/vocabulary/relators/aut51792MiAaPQMiAaPQMiAaPQBOOK9910254284203321Elliptic differential equations382567UNINA