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Numerical Methods for Partial Differential Equations I

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Numerical Methods for Partial Differential Equations I

Lecturer:  Prof.Dr. René Pinnau

Contents

In these lectures we study modelling and numerics for the three classical types of partial dif-
ferential equations: elliptic, parabolic and hyperbolic eqautions. In the first lecture we study
elliptic and parabolic equations. Hyperbolic equations will be investigated in the second lec-
ture. In the first part of the lecture we present an introduction to the theory of partial differential
equations. Subsequently, as a first approach to discretisation, we study classical finite diffe-
rence methods and their modern developments, so called compact methods. Building on the
theory of weak solutions for elliptic boundary problems, we develop and analyse finite ele-
ment discretisations. We then proceed to transfer these approaches, using the method of lines,
to the discretisation of parabolic problems.

References

D. Braess: Finite Elemente, Springer 1997 
A. Quarteroni, A. Valli: Numerical Approximation of PDEs, Springer 1994 
Ch. Grossmann, H.-G. Roos: Numerik partieller Differentialgleichungen, Teubner 2004 

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KIS

 KIS-> NumPDE I

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