Numerics of partial differential equations

International open class: IntNumPDE

Course number at LUH: 10116

Winter 2020/2021 at Leibniz University Hannover

♦News:

Sep 12, 2020: Handwritten outline


♦Overview:

This course is devoted to the numerical solution of partial differential equations (PDEs). A PDE is a function of at least two independent variables in which both derivative information and function values may appear. PDEs play a very important role in continuum mechanics for modeling applications in physics, biology, chemistry, finance, mechanical/civil/environmental engineering. The focus in this course is on numerical modeling of PDEs, which allow us to discretize them for computer simulations. We discuss various discretization schemes, design of algorithms and their rigorous numerical analysis. Moreover, we discuss the numerical solution of the arising linear equation systems. This class is an important part of scientific computing eduction in which mathematical modeling, numerical methods, and computer implementations interact.


♦Audience / Prerequisites:

The prerequisites are lectures in calculus, linear algebra and an introduction to numerics. Classes on the theory of ordinary (ODE) or partial (PDE) differential equations are useful but not mandatory. Classes in continuum mechanics may also be helpful, but are also not mandatory.


♦Time period (German winter semester):

Oct 12, 2020 - Jan 29, 2021


♦Format:

  • Self-studies with the help of the provided materials (per week materials for in total 2x90 minutes will be distributed)
  • Mixture with live elements and live discussions (approx. every two weeks on Tue or Wed, 90 minutes)
  • Weekly live exercises (90 minutes)
  • t.b.a: the online/video tool for live elements will be announced begin September 2020.



♦Workload:

  • 10 ECTS (European Credit Transfer and Accumulation System)
  • Lecture materials and live lectures: 180 minutes per week
  • Weekly exercises 90 minutes
  • Preparing individually yourself solutions to exercise questions
  • Consolidation of the contents in self studies or local team work
  • Number of classes: 26-28 lectures (L) in the entire semester
  • Number of exercises: 13-14



♦Contents:

  1. L1: Recapitulation of characteristic concepts of numerical mathematics
  2. L2-L3: Brief review of mathematical modeling of differential equations
  3. L4: Classifications
  4. L5-L8: Finite differences (FD) for elliptic boundary value problems
  5. L9-L20: Finite elements (FEM) for elliptic boundary value problems
  6. L21-L23: Numerical solution of the discretized problems
  7. L24-L26/27: Methods for parabolic and hyperbolic problems (time-dependent PDEs)
  8. L28: Recapitulation of contents
  9. If time permits: Numerical methods for nonlinear and coupled problems
L = lecture


♦Literature:

1) T. Wick; Numerical Methods for Partial Differential Equations
Hannover : Institutionelles Repositorium der Leibniz Universit├Ąt Hannover, 369 pages, 2020.
DOI: https://doi.org/10.15488/9248
Link
2) Further literature (classical/famous and more recent) can be found in Chapter 1 of Ref. 1) above
3) P. Bastian, T. Wick; PeC3 Spring School on Introduction to Numerical Modeling with Differential Equations
Hannover : Institutionelles Repositorium der Leibniz Universit├Ąt Hannover, 2019.
DOI: https://doi.org/10.15488/6427
DOI: Pre-course
DOI: Exercises
PeCCC - Peruvian Competence Center of Scientific Computing
Link



♦ Exam/Evaluation for local Hannover students:

Mid/end February 2021


♦ TAs:

Jan Philipp Thiele, Julian Roth, Max Schröder, Gina Kleinsteinberg


♦Contact:








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