Numerical Models for Differential Problems

 

Introduction.- 1 A brief survey on partial differential equations.- 2 Elliptic equations.- 3 The Galerkin finite element method for elliptic problems.- 4 Spectral methods.- 5 Diffusion-transport-reaction equations.- 6 Parabolic equations.- 7 Finite differences for hyperbolic equations.- 8 Finite elements and spectral methods for hyperbolic equations.- 9 Nonlinear hyperbolic problems.- 10 The Navier-Stokes equations.- 11 Finite element programming.- 12 Generation of 1D and 2D grids.- 13 The finite volume method.- 14 Domain decomposition method.- 15 Optimal control problems for partial differential equations.- 16 Reduced basis methods.- 17 Appendix A: Elements of functional analysis.- 18 Appendix B: Solution of algebraic systems.