Numerical Analysis of Partial Differential Equations
Sustainable Development Goals
Learning Goals
Give a solid training on numerical methods for Partial Differential Equations in terms of theory and applications.
Contents
Discretization in time and space. Finite difference method and finite element (continuous and discontinuous).
Approach problems with initial and boundary conditions. Problems of Dirichlet, Neumann and Robin. Examples of applications in 2D and 3D.
Convergence, consistency and stability.
Parabolic equations: explicit and implicit methods using finite differences and finite elements. Application to the diffusion equation.
Hyperbolic equations: quasi-linear and conservation formulations. Explicit and implicit methods using finite differences and finite elements.
Elliptic equations: methods using finite differences and finite elements.
Direct and iterative methods for solving the resulting system of equations.
Teaching Methods
Structured presentation, exemplification with emphasis on applications, problem solving, practical work in the computer lab.
Assessment
Tests during the classes, exams in the period respective, computing project, other forms to agree with the students on the first day of classes.
Recommended Reading
- R.J. LeVeque, Finite volume methods for hyperbolic problems, Cambridge University Press (2002)
- J. C. Strikwerda, Finite Difference Schemes and Partial Differential Equation, SIAM (2004)
- P.A. Raviart, J.M. Thomas, Introduction à l'Analyse Numérique des Équations aux Dérivées Partialles, Masson (1984)
- V. Girault, P.A. Raviart, Finite Element Methods for Navier-Stokes Equations, Springer (1986)
- R. Glowinski, Numerical Methods for Nonlinear Variational Problems, Springer (1984)
