LEADER 04708nam 22007215 450 001 9910254287003321 005 20200703175108.0 010 $a3-319-49316-7 024 7 $a10.1007/978-3-319-49316-9 035 $a(CKB)4100000000881606 035 $a(DE-He213)978-3-319-49316-9 035 $a(MiAaPQ)EBC6313168 035 $a(MiAaPQ)EBC5610452 035 $a(Au-PeEL)EBL5610452 035 $a(OCoLC)1007295772 035 $z(PPN)258859636 035 $a(PPN)220126054 035 $a(EXLCZ)994100000000881606 100 $a20171010d2017 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aNumerical Models for Differential Problems /$fby Alfio Quarteroni 205 $a3rd ed. 2017. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2017. 215 $a1 online resource (XVII, 681 p. 236 illus., 61 illus. in color.) 225 1 $aMS&A, Modeling, Simulation and Applications,$x2037-5255 ;$v16 311 $a3-319-49315-9 320 $aIncludes bibliographical references and index. 327 $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. 330 $aIn this text, we introduce the basic concepts for the numerical modelling of partial differential equations. We consider the classical elliptic, parabolic and hyperbolic linear equations, but also the diffusion, transport, and Navier-Stokes equations, as well as equations representing conservation laws, saddle-point problems and optimal control problems. Furthermore, we provide numerous physical examples which underline such equations. We then analyze numerical solution methods based on finite elements, finite differences, finite volumes, spectral methods and domain decomposition methods, and reduced basis methods. In particular, we discuss the algorithmic and computer implementation aspects and provide a number of easy-to-use programs. The text does not require any previous advanced mathematical knowledge of partial differential equations: the absolutely essential concepts are reported in a preliminary chapter. It is therefore suitable for students of bachelor and master courses in scientific disciplines, and recommendable to those researchers in the academic and extra-academic domain who want to approach this interesting branch of applied mathematics. 410 0$aMS&A, Modeling, Simulation and Applications,$x2037-5255 ;$v16 606 $aMathematical analysis 606 $aAnalysis (Mathematics) 606 $aNumerical analysis 606 $aMathematical models 606 $aApplied mathematics 606 $aEngineering mathematics 606 $aAnalysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12007 606 $aNumerical Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M14050 606 $aMathematical Modeling and Industrial Mathematics$3https://scigraph.springernature.com/ontologies/product-market-codes/M14068 606 $aApplications of Mathematics$3https://scigraph.springernature.com/ontologies/product-market-codes/M13003 615 0$aMathematical analysis. 615 0$aAnalysis (Mathematics). 615 0$aNumerical analysis. 615 0$aMathematical models. 615 0$aApplied mathematics. 615 0$aEngineering mathematics. 615 14$aAnalysis. 615 24$aNumerical Analysis. 615 24$aMathematical Modeling and Industrial Mathematics. 615 24$aApplications of Mathematics. 676 $a518.64 700 $aQuarteroni$b Alfio$4aut$4http://id.loc.gov/vocabulary/relators/aut$08375 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254287003321 996 $aNumerical models for differential problems$9247487 997 $aUNINA