TY  - GEN
N2  - In 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.
DO  - 10.1007/978-88-470-5522-3
DO  - doi
AB  - In 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.
T1  - Numerical models for differential problems
AU  - Quarteroni, Alfio,
ET  - Second edition.
VL  - v. 8
CN  - QA377
N1  - "Translated by Silvia Quarteroni from the original Italian edition: A. Quarteroni, Modellistica Numerica per Problemi Differenziali, 5th ed., Springer-Verlag Italia, Milano, 2012"-- t.p. verso.
ID  - 698009
KW  - Differential equations, Partial
SN  - 9788847055223 
SN  - 8847055229 
TI  - Numerical models for differential problems
LK  - https://univsouthin.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-88-470-5522-3
UR  - https://univsouthin.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-88-470-5522-3
ER  -