Numerical Models for Differential Problems
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...
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| Format: | eBook |
| Language: | English |
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Milano
Springer Milan
2009, 2009
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| Edition: | 1st ed. 2009 |
| Series: | MS&A, Modeling, Simulation and Applications
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| Online Access: | |
| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
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