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Table of Contents
1 A brief survey of partial differential equations
2 Elements of functional analysis
3 Elliptic equations
4 The Galerkin finite element method for elliptic problems
5 Parabolic equations
6 Generation of 1D and 2D grids
7 Algorithms for the solution of linear systems
8 Elements of finite element programming
9 The finite volume method
10 Spectral methods
11 Isogeometric analysis
12 Discontinuous element methods (D Gandmortar)
13 Diffusion-transport-reaction equations
14 Finite differences for hyperbolic equations
15 Finite elements and spectral methods for hyperbolic equations
16 Nonlinear hyperbolic problems
17 Navier-Stokes equations
18 Optimal control of partial differential equations
19 Domain decomposition methods
20 Reduced basis approximation for parametrized partial differential equations
References.
2 Elements of functional analysis
3 Elliptic equations
4 The Galerkin finite element method for elliptic problems
5 Parabolic equations
6 Generation of 1D and 2D grids
7 Algorithms for the solution of linear systems
8 Elements of finite element programming
9 The finite volume method
10 Spectral methods
11 Isogeometric analysis
12 Discontinuous element methods (D Gandmortar)
13 Diffusion-transport-reaction equations
14 Finite differences for hyperbolic equations
15 Finite elements and spectral methods for hyperbolic equations
16 Nonlinear hyperbolic problems
17 Navier-Stokes equations
18 Optimal control of partial differential equations
19 Domain decomposition methods
20 Reduced basis approximation for parametrized partial differential equations
References.