Degree | Type | Year | Semester |
---|---|---|---|
2500149 Mathematics | OT | 4 | 0 |
This ourse has no theoretical prerequisites, although having studied partial differential equations and / or numerical analysis will help to give context. For the practical part, there is a need of slight familiarity with the use of programming language C for scientific computing.
Partial differential equations (PDEs) are present in most mathematical models of physical processes. As with ordinary differential equations, closed formulas are available for their solution in very few cases. That is why, in almost all applications, numerical methods are required to approximate the solutions.
This course is an introduction to the numerical methods for the approximation of the solution of PDEs. It will focus on the development and analysis of finite difference methods and finite elements for "classical" equations (transport, waves, heat and potential)
1- Hyperbolic evolution problems. Finite differences schemes for the transport equation and conservation laws. The concepts of consistency, stability and convergence. The condition of Courant-Friedrichs-Lewy.
2-Parabolic evolution problems. Explicit and implicit finite differences schemes. Stability. The scheme of Crank-Nicolson.
3-Elliptical problems. Poisson problem. Stationary problems. Variational formulation. The method of Galerkin. Finite element method. Triangulations.
The classes of theory and problems will be carried out in a normal classroom of the faculty. In them the presentation of theoretical aspects of the numerical methods and their basic properties with the resolution of problems of a theoretical nature will be undertaken. Students will work on lists of problems that will be provided throughout the course.
The practical classes will be carried out in a computer classroom of the faculty. During these sessions, students will solve some applied type problem through the implementation in a programming language of some of the methods studied in the subject. These practical sessions will be evaluated from the delivery at the end of the course (the date will be announced) of the code and a practical report.
Title | Hours | ECTS | Learning Outcomes |
---|---|---|---|
Type: Directed | |||
Exercise classes | 10 | 0.4 | 1, 2, 3, 6, 5, 4 |
Practical classes | 14 | 0.56 | 1, 2, 3, 6, 5, 4 |
Theory classes | 26 | 1.04 | 1, 2, 3, 6, 4 |
Type: Autonomous | |||
Problems solving and practices | 44 | 1.76 | 1, 2, 3, 6, 5, 4 |
Study | 50 | 2 | 1, 2, 3, 6, 4 |
Title | Weighting | Hours | ECTS | Learning Outcomes |
---|---|---|---|---|
Final exam | 0.4 | 3 | 0.12 | 1, 2, 3, 5, 4 |
Partial exam | 0.25 | 3 | 0.12 | 1, 2, 3, 5, 4 |
Practice delivery | 0.35 | 0 | 0 | 1, 2, 6, 5, 4 |
Bibliography
Aditional bibliography