Simulación numérica de problemas de EDP sobre dominios complejos

Curso electivo y Seminario avanzado de Matematicas I: MA691 (DIM) - CC60X (DCC)

March 2008

Course instructors:

Office: 622, CMM-DIM
Office hours: MWF at 2pm or by appointment
Phone: 978 4802 (office)

if you send an email, please put MA691 or CC60X in the subject

0. Schedule

Lecture: Mon 14:30 - 17:45room: B213 (2nd floor)
Computer exps: Fri 16:15 - 17:45

1. Syllabus

MA691 (CC60X) is an introduction to mathematical and numerical methods for the simulation of complex problems modelled using partial differential equations. We will cover basic theoretical results, and we will apply these results in numerical analysis projects in a computing environment.

2. References

  1. D. Braess, Finite elements, Cambridge University Press, (1997).
  2. H. Brezis, Analyse fonctionnelle: théorie et applications, Dunod, (2005).
  3. P.G. Ciarlet, The Finite Element Method, North Holland, (1978).
  4. A. Ern and J.L. Guermond, Theory and practice of finite elements, vol. 159 of Applied Mathematical Series, Springer-Verlag, New York, (2004).
  5. L.C. Evans, Partial differential equations, AMS, (2002).
  6. P. Frey and P.L. George, Mesh generation: application to finite elements, 1st edition, Hermès Science, (2000).
  7. V. Girault and P.A. Raviart, Finite element methods for Navier-Stokes equations, Springer Series in Computational Mathematics, 5, Springer, (1986).
  8. G.H. Golub and F. Van Loan, Matrix computations, 3rd edition, The Johns Hopkins University Press, (1993).
  9. R.J. LeVeque, Numerical methods for conservation laws, Birkhauser, Basel, (1992).
  10. K.W. Morton and D. Mayers, Numerical solution of partial differential equations, 2nd edition, Cambridge University Press, (2005).
  11. J.T. Oden and J.N. Reddy, An introduction to the mathematical theory of finite element methodsn vol 2, Handbook of numerical analysis, North Holland, (1991).
  12. A. Quarteroni, R. Sacco, F. Saleri, Numerical Mathematics, Springer, (2000).
  13. W. Rudin, Functional analysis, 2nd edition, Mc Graw Hill, (1991).
  14. P. Solin, Partial differential equations and the finite element method, Wiley-Interscience, (2005).
  15. K. Yosida, Functional analysis, 6th edition, Springer-Verlag, (1980).

3. Grading policy

Your course grade will be determined by your assignment grades. The assignments will be homeworks, projects and two exams (midterm and final). The project will culminate in presentations and a written report.
Tentative grading scheme: 0.6 max(E,(E+C)/2) + 0.4 TP
where C denotes the midterm exam and homeworks, E the final exam and TP corresponds to the final project.

4. Homework

4. Projects

Updated 2008-04-03 12:11 CLT