The mathematical modeling of many processes in nature and industry leads to partial differential equations. Generally, such equations cannot be solved analytically. It is only possible to compute numerical approximations to the solution on the basis of discretized equations. This course studies discretizations of elliptic partial differential equations. Major topics are finite difference methods and finite element methods.

• F. John: Partial Differential Equations. Springer (1982)
• M. Renardy, R. C. Rogers: An introduction to partial differential equations, Springer, 2. Auflage (2004)
• A. Quarteroni, R. Sacco, F. Saleri: Numerische Mathematik 2. Springer (2002)
• D. Braess: Finite Elemente. Springer, 3. Auflage (2002)
• P. A. Raviart, J. M. Thomas: Introduction à l'analyse numérique des équations aux dérivées partielles, Dunod (1998)

Prerequisites

Prerequisites for this course are basic knowledge in calculus (Analysis I-III) and Numerical Analysis (Numerik I). Some knowledge in Functional Analysis will help a lot.