Syllabus for |
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| TMA482 - Partial differential equations - computing science |
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| Owner: TM |
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5,0 Credits (ECTS 7,5) |
| Grading: TH - Five, Four, Three, Not passed |
| Level: C |
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Department: 11 - MATHEMATICAL SCIENCES
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Teaching language: English
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Credit distribution |
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Examination dates |
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Sp1 |
Sp2 |
Sp3 |
Sp4 |
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No Sp |
| 0101 |
Examination |
5,0 c |
Grading: TH |
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5,0 c
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16 Mar 2007 am M, |
22 Aug 2007 am V |
In programs
CEMAS MSc PROGRAMME IN COMPUTATIONAL AND EXPERIMENTAL TURBULENCE, Year 1 (elective)
TTFYA ENGINEERING PHYSICS, Year 4 (elective)
TM Teknisk matematik, Year 2 (elective)
EMMAS MSc PROGR IN ENGINEERING MATHEMATICS, Year 1 (elective)
TKEFA CHEMICAL ENGINEERING WITH ENGINEERING PHYSICS, Year 4 (elective)
Examiner:
Professor Claes Johnson
Eligibility:
For single subject courses within Chalmers programmes the same eligibility requirements apply, as to the programme(s) that the course is part of.
Course specific prerequisites
TMA371 Partial differential equations TM or the equavalent (for ex. Partial differential equations F)
Aim
The purpose of the course is to extend the compu-tational techniques met in the introductory course Partial differential equations TM to non linear problems, to cover important areas of application such as convection-diffusion-reaction, fluid flow, and elasticity-plasticity problems, and related inverse and optimization problems. Understanding the stability properties of the problems and methods under consideration is of particular concern in the course.
Content
Time integration using cG(q) and dG(q) methods, error analysis using residuals and dual problems, finite elements methods for non-linear Poisson type problems and systems of convection-diffusion-reaction equations, Burgers' equation and shock wave solutions, rarefaction waves and the entrophy condition, Navier-Stokes equations for incompres-sible flow, hydrodynamic stability, stabilized finite element methods, elasticity-plasticity problems, examples of inverse problems and optimization problems related to pde models.
The course is given in English normally.
Literature
K. Eriksson, D. Estep, P. Hansbo, and C. Johns-son, Computational Differential Equations, Student-litteratur/Cambridge University Press, 1996.
Parts of Advanced Computational Differential Equations.
Examination
Assignments during the course, including both theory and computation.