Numerical Methods for Partial Differential Equations II
Summer term 2021

(Lectures and tutorials)

Lecturers

Learnweb

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Contents

Partial differential equations are equations that comprise a connection between a function, its partial derivatives and further given functions. Many applications in physics, engineering, biology oder medicine can be modeled using such partial differential equations. This lecture covers the numerical analysis of conservation laws. Typical examples from physics are for instance the conservation of mass, momentum or energy. We examine convergence properties of finite difference and finite volume schemes for scalar equations. A short introduction to the theory and numerics of systems of conservation laws rounds out the lecture.

Literature

  • T. Barth und M. Ohlberger. Finite volume methods: foundation and analysis. In T.J.R. Hughes E. Stein, R. de Borst, editor, Encyclopedia of Computational Mechanics , volume 1, chapter 15. John Wiley & Sons, Ltd, 2004.
  • R. Eymard, T. Galluoët und R. Herbin. Finite volume methods. In Handbook of numerical analysis, Vol. VII , pages 713-1020. North-Holland, Amsterdam, 2000.
  • D. Kröner. Numerical schemes for conservation laws . Wiley-Teubner Series Advances in Numerical Mathematics. John Wiley & Sons Ltd., Chichester, 1997.