Numerical Models for Differential Problems

• Main Author: Quarteroni, Alfio (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Milano : Springer Milan, 2009.
• Series: MS&A ; 2
• Subjects: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Applied mathematics.; Engineering mathematics.; Computer mathematics.; Numerical analysis.; Mathematical models.; Analysis.; Mathematics, general.; Numerical Analysis.; Mathematical Modeling and Industrial Mathematics.; Applications of Mathematics.; Computational Mathematics and Numerical Analysis.

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 l...

Table of Contents:

• A brief survey on partial differential equations
• Elements of functional analysis
• Elliptic equations
• The Galerkin finite element method for elliptic problems
• Parabolic equations
• Generation of 1D and 2D grids
• Algorithms for the solution of linear systems
• Elements of finite element programming
• The finite volume method
• Spectral methods
• Diffusion-transport-reaction equations
• Finite differences for hyperbolic equations
• Finite elements and spectral methods for hyperbolic equations
• Nonlinear hyperbolic problems
• Navier-Stokes equations
• Optimal control of partial differential equations
• Domain decomposition methods
• Reduced basis approximation for parametrized partial differential equations.