Lecturer:
Óscar Angulo (Universidad de Valladolid)

Board Contact:
Dimitri Breda

The course consists of an introduction about the fundamental concepts, theory and computational techniques used to obtain numerical solutions of partial differential equations (PDEs). By the end of the course, students will be able to

• formulate numerical discretization of PDEs;
• understand and formulate stability, consistency, and convergence analysis, at least for linear models;
• implement basic finite difference, finite element and finite volume schemes;
• learn about other techniques: method of lines, collocation, Galerkin and Ritz-Galerkin methods, spectral methods.

Bibliography:

• R. J. Leveque, Finite Difference Methods for Ordinary and Partial Differential Equations, SIAM, Philadelphia, 2007.
• J. C. Strikwerda, Finite Difference Schemes and Partial Differential Equations, SIAM Philadelphia, 2004.
• H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, Springer, 2011.
• P. A. Raviart, J. M. Thomas, Introduction a l’Analyse Numerique des Equations aux Derivees Partielles, Masson, París, 1988.
• C. Johnson, Numerical solutions of partial differential equations by the finite element method, Cambridge University Press, 1987.
• A. Quarteroni, Numerical Models for Differential Problems, Series: MSA, Vol 2, 2009.
• S. Larsson, V. Thomee, Partial Differential Equations with Numerical Methods, 2004, Springer.