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Syllabus for

Academic year
TMA482 - Partial differential equations - computing science
 
Owner: TM
5,0 Credits (ECTS 7,5)
Grading: TH - Five, Four, Three, Not passed
Level: C
Department: 11 - MATHEMATICAL SCIENCES


Teaching language: English

Course module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 No Sp
0101 Examination 5,0 c Grading: TH   5,0 c   16 Mar 2007 am M,  22 Aug 2007 am V

In programs

TM Teknisk matematik, Year 2 (elective)
EMMAS MSc PROGR IN ENGINEERING MATHEMATICS, Year 1 (elective)
TTFYA ENGINEERING PHYSICS, Year 4 (elective)
CEMAS MSc PROGRAMME IN COMPUTATIONAL AND EXPERIMENTAL TURBULENCE, 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.


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