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Bergische Universität Wuppertal
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Bergische Universität Wuppertal
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Univ.-Prof. Dr. Matthias Ehrhardt Prof. Dr. Pavel Petrov Petr Petrov, M.Sc. |
Schedule
Consultation Hours for exam:
Lecture (Pavel Petrov)
Mon, 14:15 - 15:45
Hörsaal 5, Gebäude G.10.07
Date: weekly, starting April 14
Lecture (Matthias Ehrhardt)
Tue, 14:15 - 15:45
Hörsaal 6, Gebäude G.10.06
Date: weekly, starting April 15
Exercise (Petr Petrov)
Thu, 12:15 - 13:45
Hörsaal 7, Gebäude G.10.05
Date: weekly, starting April 17
Consultation Hours (Ehrhardt)
by appointment
Room G.13.23
Date: May, June, July
Consultation Hours (Pavel Petrov)
by appointment
Room G.14.22
Date: May, June, July
Consultation Hours (Petr Petrov)
Mon, ???
Room G.13.24
Date: May, June, July
Content:
The lecture deals with the numerical solution of partial differential equations and the estimation of
the error between continuous and discrete solution. We will first study classical finite difference methods for
parabolic and elliptic problems and their modern further development, the so-called compact methods, with respect
to consistency, stability and convergence.
After an introduction to the theory of Sobolev spaces, finite element discretizations are developed and analyzed
based on the weak solution theory of elliptic boundary value problems. Subsequently, multigrid methods for
solving the resulting systems of equations are discussed. The lecture concludes with a brief outline of boundary element methods.
The focus is on the connection of theory, numerical analysis and practical implementation issues by means of
programs in an accompanying practical course. The students are familiarized with
free software in an integrative way:
while most of the programming tasks are implemented with GNU Octave
/ Scilab , the symbolic software Maxima
is used to design a tool which determines the resulting mass and stiffness matrices for a variety of approach and test functions.
Matlab, GNU Octave and Scilab, respectively, are recommended for the implementation of the practical tasks.
In addition to the use of dedicated learning software for finite elements
(CALFEM) and multigrid methods (MGLab),
the use of Matlab PDE Toolbox,
NMLibforOctave and
Scilab finite element toolbox FreeFEM will be learned.
Partial differential equations arise frequently in the modeling of physical, chemical, or biological phenomena.
Topics of the Lecture:
Target Audience:
Remarks:
Pre-Knowledge:
Analysis I-II, Linear Algebra I-II, Introduction to Numerical Mathematics.
Numerics of ODEs is helpful.
Lecture Notes:
Literature:
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