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000801339 019__ $$a1008972770$$a1009044864$$a1009526123
000801339 020__ $$a9783319493169$$q(electronic book)
000801339 020__ $$a3319493167$$q(electronic book)
000801339 020__ $$z9783319493152
000801339 020__ $$z3319493159
000801339 0247_ $$a10.1007/978-3-319-49316-9$$2doi
000801339 035__ $$aSP(OCoLC)on1007295772
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000801339 050_4 $$aQA377$$b.Q83 2017eb
000801339 08204 $$a518/.64$$223
000801339 1001_ $$aQuarteroni, Alfio,$$eauthor.
000801339 24510 $$aNumerical models for differential problems /$$cAlfio Quarteroni.
000801339 250__ $$aThird edition.
000801339 264_1 $$aCham, Switzerland :$$bSpringer,$$c2017.
000801339 300__ $$a1 online resource (xvii, 681 pages) :$$billustrations.
000801339 336__ $$atext$$btxt$$2rdacontent
000801339 337__ $$acomputer$$bc$$2rdamedia
000801339 338__ $$aonline resource$$bcr$$2rdacarrier
000801339 347__ $$atext file$$bPDF$$2rda
000801339 4901_ $$aMS&A,$$x2037-5255 ;$$vvolume 16
000801339 504__ $$aIncludes bibliographical references.
000801339 5050_ $$a1 A brief survey of partial differential equations -- 2 Elements of functional analysis -- 3 Elliptic equations -- 4 The Galerkin finite element method for elliptic problems -- 5 Parabolic equations -- 6 Generation of 1D and 2D grids -- 7 Algorithms for the solution of linear systems -- 8 Elements of finite element programming -- 9 The finite volume method -- 10 Spectral methods -- 11 Isogeometric analysis -- 12 Discontinuous element methods (D Gandmortar) -- 13 Diffusion-transport-reaction equations -- 14 Finite differences for hyperbolic equations -- 15 Finite elements and spectral methods for hyperbolic equations -- 16 Nonlinear hyperbolic problems -- 17 Navier-Stokes equations -- 18 Optimal control of partial differential equations -- 19 Domain decomposition methods -- 20 Reduced basis approximation for parametrized partial differential equations -- References.
000801339 506__ $$aAccess limited to authorized users.
000801339 520__ $$aIn this text, we introduce the basic concepts for the numerical modelling of partial differential equations. We consider the classical elliptic, parabolic and hyperbolic linear equations, but also the diffusion, transport, and Navier-Stokes equations, as well as equations representing conservation laws, saddle-point problems and optimal control problems. Furthermore, we provide numerous physical examples which underline such equations. We then analyze numerical solution methods based on finite elements, finite differences, finite volumes, spectral methods and domain decomposition methods, and reduced basis methods. In particular, we discuss the algorithmic and computer implementation aspects and provide a number of easy-to-use programs. The text does not require any previous advanced mathematical knowledge of partial differential equations: the absolutely essential concepts are reported in a preliminary chapter. It is therefore suitable for students of bachelor and master courses in scientific disciplines, and recommendable to those researchers in the academic and extra-academic domain who want to approach this interesting branch of applied mathematics.--$$cProvided by publisher.
000801339 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed October 24, 2017).
000801339 650_0 $$aDifferential equations, Partial$$xNumerical solutions.
000801339 77608 $$iPrint version:$$z3319493159$$z9783319493152$$w(OCoLC)960835751
000801339 830_0 $$aMS&A (Series) ;$$vv.16.$$x2037-5255
000801339 852__ $$bebk
000801339 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-3-319-49316-9$$zOnline Access$$91397441.1
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