Unit description:

The aim of this Research Unit is to present an introduction to several methods for solving PDEs. More precisely, the finite element method for elliptic and parabolic equations and the finite volume method for hyperbolic systems will be considered, as well as the high-order extensions of the latter one. The mathematical and numerical aspects will be addressed as well as the implementation.

The lectures will be complemented by practical sessions during which the students will implement the numerical methods in the computer and apply them to academic examples.

The students are expected to learn what are the methods better suited to the PDE to be solved, what are their mathematical properties and how to implement them.

Course program:

  • The Finite Element Method for elliptic equations: Laplace and Poisson equations.
  • The Finite Element Method for parabolic equations: the heat equation.
  • The Finite Volume Method for conservation laws: Burgers equation and traffic models.
  • Second-order methods for conservation laws: MUSCL and other reconstruction operators.

Lectures:

  • Carlos Parés Madroñal (Universidad Málaga)
  • Enrique D. Fernández Nieto (Universidad de Sevilla)
  • Juan Vicente Gutiérrez Santacreu (Universidad de Sevilla)

Conference Speakers:

  • Santiago Badia (Universitat Politècnica de Catalunya). Title: TBA: Friday, 13 April, 15:30 - 16:30.
  • Michael Dumbser (University of Trento, Italy). Title: TBA. Monday, 17 April, 15:30 - 16:30.

Schedule of the Course 3:

  • Thursday, April 12 9:30 - 11:00 (Juan Vicente Gutiérrez Santacreu) and 11:30-13:00 (Rafael Rodríguez)
  • Friday, April 13: 9:30 - 11:00 (Juan Vicente Gutiérrez Santacreu) and 11:30-13:00 (Rafael Rodríguez)
  • Monday, April 16: 9:30 - 11:00 (Tomás Morales de Luna) and 11:30-13:00 (Carlos Parés)
  • Tuesday, April 17: 9:30 - 11:00 (Tomás Morales de Luna) and 11:30-13:00 (Carlos Parés)