Content:

Mathematical modelling of spatial or spatial/temporal phenomena such as porous medium flow, solidification of melts, weather prediction, etc. typically leads to partial differential equations (pdes). After some remarks on the modelling with and classification of pdes, the course will concentrate on elliptic problems. Starting with a brief introduction to the classical theory (existence and uniqueness of solutions, Green's functions) and assiciated difference methods we will mainly focus on weak solutions and their approximation by finite element methods. Adaptivity and multigrid methods will be also discussed.

• 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.