LEADER 04864nam 22008055 450 001 9910510542403321 005 20251223172416.0 010 $a3-030-79385-0 024 7 $a10.1007/978-3-030-79385-2 035 $a(MiAaPQ)EBC6809652 035 $a(Au-PeEL)EBL6809652 035 $a(CKB)19919501000041 035 $a(OCoLC)1287129712 035 $a(PPN)258839198 035 $a(BIP)82317641 035 $a(BIP)80380344 035 $a(DE-He213)978-3-030-79385-2 035 $a(EXLCZ)9919919501000041 100 $a20211119d2021 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aNumerical Methods for Elliptic and Parabolic Partial Differential Equations $eWith contributions by Andreas Rupp /$fby Peter Knabner, Lutz Angermann 205 $a2nd ed. 2021. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2021. 215 $a1 online resource (811 pages) 225 1 $aTexts in Applied Mathematics,$x2196-9949 ;$v44 311 08$aPrint version: Knabner, Peter Numerical Methods for Elliptic and Parabolic Partial Differential Equations Cham : Springer International Publishing AG,c2022 9783030793845 327 $aFor Example: Modelling Processes in Porous Media with Differential Equations -- For the Beginning: The Finite Difference Method for the Poisson Equation -- The Finite Element Method for the Poisson Equation -- The Finite Element Method for Linear Elliptic Boundary Value Problems of Second Order -- Grid Generation and A Posteriori Error Estimation -- Iterative Methods for Systems of Linear Equations -- Beyond Coercivity, Consistency and Conformity -- Mixed and Nonconforming Discretization Methods -- The Finite Volume Method -- Discretization Methods for Parabolic Initial Boundary Value Problems -- Discretization Methods for Convection-Dominated Problems -- An Outlook to Nonlinear Partial Differential Equations -- Appendices. 330 $aThis graduate-level text provides an application oriented introduction to the numerical methods for elliptic and parabolic partial differential equations. It covers finite difference, finite element, and finite volume methods, interweaving theory and applications throughout. The book examines modern topics such as adaptive methods, multilevel methods, and methods for convection-dominated problems and includes detailed illustrations and extensive exercises. For students with mathematics major it is an excellent introduction to the theory and methods, guiding them in the selection of methods and helping them to understand and pursue finite element programming. For engineering and physics students it provides a general framework for the formulation and analysis of methods. This second edition sees additional chapters on mixed discretization and on generalizing and unifying known approaches; broader applications on systems of diffusion, convection and reaction; enhanced chapters on node-centered finite volume methods and methods of convection-dominated problems, specifically treating the now-popular cell-centered finite volume method; and the consideration of realistic formulations beyond the Poisson's equation for all models and methods. 410 0$aTexts in Applied Mathematics,$x2196-9949 ;$v44 606 $aNumerical analysis 606 $aMathematical analysis 606 $aMathematics 606 $aMathematics$xData processing 606 $aMathematical physics 606 $aEngineering mathematics 606 $aEngineering$xData processing 606 $aNumerical Analysis 606 $aAnalysis 606 $aApplications of Mathematics 606 $aComputational Mathematics and Numerical Analysis 606 $aTheoretical, Mathematical and Computational Physics 606 $aMathematical and Computational Engineering Applications 615 0$aNumerical analysis. 615 0$aMathematical analysis. 615 0$aMathematics. 615 0$aMathematics$xData processing. 615 0$aMathematical physics. 615 0$aEngineering mathematics. 615 0$aEngineering$xData processing. 615 14$aNumerical Analysis. 615 24$aAnalysis. 615 24$aApplications of Mathematics. 615 24$aComputational Mathematics and Numerical Analysis. 615 24$aTheoretical, Mathematical and Computational Physics. 615 24$aMathematical and Computational Engineering Applications. 676 $a515.353 700 $aKnabner$b Peter$0149470 702 $aAngermann$b Lutz 702 $aRupp$b Andreas 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910510542403321 996 $aNumerical methods for elliptic and parabolic partial differential equations$92905046 997 $aUNINA