Analisis Numerico de Ecuaciones en Derivadas parciales

Curso MA53L-1 (DIM)

Semestre de Primavera 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 MA53L-1 in the subject

0. Schedule

Lecture: Tue-Thu 10:15 - 11:45room: F9
Computer exps: Fri 14:30 - 17:45room: B214

1. Syllabus

MA53L-1 is an introduction to mathematical and numerical methods for the resolution of partial differential equations: finite differences, finite elements and finite volume methods. We will cover basic theoretical results, and we will apply these results in numerical analysis projects.
Details of the Syllabus (PDF file)

2. References

  1. G. Allaire, Analyse numérique et optimisation, Editions de l’Ecole Polytechnique, Paris, 2006.
  2. I. Babuska, A. K. Aziz, Foundations of the finite element method, In A. K. Aziz, editor, The Mathematics Foundations of the Finite Element Method with Applications to Partial Differential Equations, 3–362, Academic Press, New York, 1972.
  3. C. Bernardi, Y. Maday, F. Rapetti, Discrétisations variationnelles de problèmes aux limites elliptiques, Mathématiques et Applications, vol. 45, Springer, Paris, 2004.
  4. S. Brenner, L.-R. Scott, The mathematical theory of finite element method, Springer, 2000.
  5. J.-H. Bramble, S.-R. Hilbert, Estimations of linear functionals on Sobolev spaces with application to Fourier transform and spline interpolation, SIAM J. Numer. Anal., 25(6), 1237–1271, 1970.
  6. H. Brezis, Analyse fonctionnelle: théorie et applications, Dunod, (2005).
  7. Z. Cai, On the finite volume element method, Numer. Math. 58, 713–735, 1991.
  8. P.G. Ciarlet, The Finite Element Method, North Holland, (1978).
  9. R. Dautray, J.-L. Lions, Analyse mathématique et calcul numérique, Tomes 3, 4, Masson, 1987.
  10. A. Ern and J.L. Guermond, Theory and practice of finite elements, vol. 159 of Applied Mathematical Series, Springer-Verlag, New York, (2004).
  11. L.C. Evans, Partial differential equations, AMS, (2002).
  12. R. Eymard, T. Gallouet, R. Herbin, The Finite Volume Method, Handbook of Numerical Analysis, Ph. Ciarlet J.L. Lions eds, North Holland, 2000, 715-1022
  13. M. Krizek, P. Neittaanm¨aki, Finite element approximation of Variational Problems and Applications, London, Longman, 1990.
  14. J. Necas, Les méthodes directes dans la théorie des équations elliptiques, Academia, Prague, 1967.
  15. K.W. Morton and D. Mayers, Numerical solution of partial differential equations, 2nd edition, Cambridge University Press, (2005).
  16. A. Quarteroni, R. Sacco, F. Saleri, Numerical Mathematics, Springer, (2000).
  17. P.-A. Raviart, J.-M. Thomas, Introduction à l’analyse numérique des équations aux derivées partielles, Masson, 1998.
  18. P. Solin, Partial differential equations and the finite element method, Wiley-Interscience, (2005).
  19. A. Tveito and R. Winther, Introduction to partial differential equations: a computational approach, Texts in Applied Mathematics, 29, Springer, 1998.
  20. O. Zienkiewicz, J.-Z. Zhu, R-L. Taylor, The Finite Element Method: Its Basis and Fundamentals, Elsevier, Paris, 2005.

3. Grading policy

Grading for the class is based on the results of assessments as follows:
Exam 50 % (3 controls), Projects 30 % (2 projects), TP 20% (4 numerical exp.)

4. Homework

4. Projects

Updated 2008-07-29 15:08 CLT