TY - BOOK
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
DA - 2009
AU - Quarteroni, Alfio
PB - Springer
PP - Heidelberg, DE
N1 - Written for students of bachelor and master courses in scientific disciplines: engineering, mathematics, physics, computational sciences, and information science
ID - 140685
KW - Analysis
KW - Numerical modelling
KW - PDE
SN - 978-88-470-1070-3
UR - http://www.springer.com/math/book/978-88-470-1070-3
ER -