SoSe 20: Basic Module: Numerics III
Ralf Kornhuber
Additional information / Pre-requisites
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. <!-- This lecture will be accompanied by a seminar on "Finite Elements" and a Summerschool both held in block form, probabely in late September. -->
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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.
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- 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)
24 Class schedule
Regular appointments
Content:
Mathematical modelling of spatial or spatial/temporal phenomena such as porous medium flow, solidification of melts, weather prediction, etc. typically leads to partial ... read more