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250048 VO Numerics of Partial Differential Equations (2020W)

6.00 ECTS (4.00 SWS), SPL 25 - Mathematik

Registration/Deregistration

Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

Classes will take place online on the Moodle platform.

Monday 05.10. 10:00 - 13:00 Digital
Monday 12.10. 10:00 - 13:00 Digital
Monday 19.10. 10:00 - 13:00 Digital
Monday 09.11. 10:00 - 13:00 Digital
Monday 16.11. 10:00 - 13:00 Digital
Monday 23.11. 10:00 - 13:00 Digital
Monday 30.11. 10:00 - 13:00 Digital
Monday 07.12. 10:00 - 13:00 Digital
Monday 14.12. 10:00 - 13:00 Digital
Monday 11.01. 10:00 - 13:00 Digital
Monday 18.01. 10:00 - 13:00 Digital
Monday 25.01. 10:00 - 13:00 Digital

Information

Aims, contents and method of the course

The course mainly focuses on Finite Element Methods for the numerical approximation of Partial Differential Equations. Three aspects of the finite element method will be considered: i) theoretical foundations, ii) examples of applications to the numerical approximation of partial differential equations arising in different application domains, iii) implementation details. After revising some basic concepts in functional analysis, finite element methods for the Poisson problem will be introduced; their stability and error analysis, as well as the basic tools for their implementation, will be presented. Then, finite element approximations of the heat equation, of the Helmholtz problem and of advection-dominated advection-diffusion problems will be considered, discussing the respective specific issues. Implementation details will be discussed. The last part of this course, depending on the students' interests, will concern either other applications (fluid mechanics, electromagnetics, elasticity), or non standard finite element methods (as discontinuous Galerkin methods).

Assessment and permitted materials

Final oral exam (in case that presence examination is not possible, the exam will be online).

Minimum requirements and assessment criteria

Presentation of theoretical and numerical aspects of Finite Element Methods for the numerical approximation of Partial Differential Equations arising from different applications.

Examination topics

Content of the lectures.

Reading list

Suggested reading: A. Quarteroni, Numerical Models for Differential Problems, Springer, 2014. Additional material and course notes will be distributed during the course.

Course website: https://mat.univie.ac.at/~perugia/TEACHING/NMPDEWS2020/nmpde2020.html

Association in the course directory

MANV, MAMV

Last modified: We 05.05.2021 08:08