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Finite Element Methods

Information for fem07

The goal of this course is to give basic knowledge of the theory and practice of the finite element method and its application to the partial differential equations of physics and engineering sciences. The purpose is to give a balanced combination of theoretical and practical skills. The theoretical part is mainly concerned with the derivation of finite element formulations as well as estimating the discretization error and how to use error estimates to adaptively refine the mesh (see the FEniCS gallery and the Body and Soul gallery). The practical part deals with computer implementation: element matrices, assembly, numerical integration, etc.

Course Home Page

All relevant information for the course is available on the course homepage; such as this project pm, lecture plan, extra problems with solutions, old exams, etc. The homepage will be continuously updated during the course. Be sure to check back regularly for up to date information, schedule changes, lab report feedback, etc: http://www.csc.kth.se/utbildning/kth/kurser/DN2260/fem07/

News

080401: NO APRIL'S FOOL JOKE: Corrected date! Next examination paper will be Sat April 26 (twenty-six) 9-14, Osquars B. 2. IF you have planned for April 19 and can't make April 26, call me. The outer door will be open. Go to floor 5 and ring the bell, or phone 0730 843451.

080123: Next examination paper will be Sat Jan 26, 9-14, Osquars B. 2. The outer door will be open. Go to floor 5 and ring the bell, or phone 0730 843451.

071218: Next examination paper will be Fri Jan 25 or Sat Jan 26, 9-14, Pls. let me know which is best!

071205: Examination paper Dec 8, 9-14, in 4523. Pls. use entrance Lindstedtsv 3 if Osquars B 2 is locked

News

071106:

Grading scheme DN2260 Finite Elements Fall 07 pdf here

Exam paper Oct 25 pdf here

Homework & project reports are kept at the Student Office (Osq. B 2, bottom floor)

Next examination paper prel. Dec 8, 9-14, and then mid-january, 2008. Pls. let me know asap if Dec 8 is inconvenient.

071013:

Hints about completion of mesh refinement, the disc brake problem suggestion for Project B:4, etc.pdf here

Extra lecture Mon Oct 15 9(15)- 11 (or so) K53 (Chemistry building, just north of Nada)

Summing up, convection diffusion, review.

Extra Problem solving class Tue Oct 16 9(30) - 11 (or so), E33

Old exam paper, review,

Questions & Answers, Thu Oct 18 15 --, E33

More examples of exam. questions,

070925:

Office hours changed, see below. A page or two of lecture notes will appear here ASAP. Please hand in solutions to problem set A and project A before Monday (official deadline Friday). It will be possible to hand in completions later.

070924:

!! LECTURE TOMORROW TUE, SEP 25 13-15 in 1537, Osquars B 2, 5th floor, to the right.

070916:

!! LECTURE TOMORROW MON, SEP 17 13-15 CANCELLED!! Re-scheduling by agreement with students at the close of problem solving class Wed Sep 19.

070904: Register for the course by the RES-system, see below. Note: The dialogue is in Swedish, ask fellow Swedish student if necessary. There is only one group, say group 1.

070904: First part of lecture 1 pdf here.

070830: Course home page 07 on line, still under construction. Course starts Monday September 3, 13-15, in D34. Schedule, see below, or :pdf here

Registration

To register for this course you need to use the RES-system: in a Nada UNIX terminal window, give the command
>res checkin fem07

Instructors

Jesper Oppelstrup; email: jespero@csc.kth.se , course responsible.
Sara Zahedi; email: sara7@csc.kth.se
Murtazo Nazarov; email: murtazo@csc.kth.se

Office Hours

Jesper Oppelstrup (room 1523): Mon 9-10
Murtazo Nazarov (room 4520): Wed 10-11; This week only: Thu 9-10, Fri 9-10
Sara Zahedi (room 4526): Thu 9-10; This week only: Fri 9-10 )
Classes in the course have priority over office hours.

Instruction

9x2h Lectures, 7x2h problem solving ÒexerciseÓ classes, and 6x2h computer lab sessions. The instructors will generally make themselves available to students and answer questions, help with problems, etc., for the duration of the course. When they have more pressing immediate matters to attend to a later meeting can be scheduled. Students are encouraged to collaborate, in studying the theory as well as doing homework and computer labs and are expected to adhere to the CSC code of honor, accessible on the CSC student home page: Mindless copying of others' homework and computer codes will be persecuted.

Examination

The final grade of this course will be the mean value of the grade of a written exam and a project (rounded up):
(1) Written exam: Open book, five hours. Old exam papers available on the home page, first paper given Thursday October 25, 14-19, M31, M32.

(2) Project: ProjA and ProjB use the Puffin FE software to experiment with different equations, mesh refinements, etc. The project should be carried out individually or in groups of two, and a report submitted by the deadline for each of ProjA and B. See the Project PM.


2 sets of homework problems generate maximum 5 bonus points for the written exam if handed in by the deadlines. No more than two students per solution handed in.
Problem set A: 8.13, 15.19, 15.20, 15.21, 15.22

Problem set B: 8.22, 15.45(a,b), 15.48, 15.49, 21.8
Important: Policy regarding deadlines for projects and problem sheets: Deadlines: ProjA and ProbA: Fri, Sept. 28, ProjB and ProbB: Fri Oct. 19 15:00. Minor complementing material for ProjA and ProbA are allowed until Friday October 19th at 15.00, a deadline which will be enforced: Past deadline, any solutions to Problems are ignored (= no bonus points for the written exam), and any project reports can give maximum grade 3. Bonus points are only good for the exam paper october 25 and the first re-exam (time to be determined).

Course evaluation form

Please fill out the course evaluation form after the written exam.
Press here to get course evaluation form:
The following message means that your submitted form has been received: Din utvärdering har tagits emot. Tack för hjälpen!

Result of course evaluation.

Literature

Course book (CDE)

"K. Eriksson, D. Estep, P. Hansbo, C. Johnson: Computational Differential Equations",

Studentlitteratur, ISBN ISBN 91-44-49311-8. Price: 410 kr at kårens bokhandel.

Hints and solutions to some of the problems in the book.

Useful inequalities.

More books in the same series.

Project

Project PM

Part A deadline: Friday September 28

Part B deadline: Friday October 19 15.00 - WILL BE ENFORCED!

First page of reports should include: in BIG letters: course code and name of grader (DN2260 Murtazo Nazarov); name, email and study program for all group members. Submit electronically (pdf, not word) to Murtazo or paper in the CSC mailbox outside Delfi, bottom floor, Osquars B. 2.

Using your own computer: Matlab is available at the library, and the PDE-toolbox is available to download for free. Detailed information on the mesh representation available here.

Computer Sessions (F1-F5 tutorial for the project)
Puffin (used in the project)
Puffin Manual
DOLFIN (big brother of Puffin)
FEniCS (software project including both Puffin and DOLFIN)
Body and Soul (educational project including Puffin sessions, CDE book, other books,...)

Laplacian models (AMBS) (some PDE applications)
Robin boundary conditions
Robin boundary conditions in 2D

Triangle

Extra material

Old exams from KTH with solutions: aug06, jan06, dec05, dec02, feb03, maj03
Old exams from Chalmers: 00a, 00c, 01c, 02c, 03a, with solutions: 00a, 00c, 01c, 02c, 03a
Extra exercises:
Exercises (E1a) with solutions
Exercises (E1b) with solutions
Exercises (E2) with solutions
Exercises (E3) with solutions
Exercises (E4) (in swedish) with solutions
Problems (P1) (in swedish) with solutions

Further reading

H.P. Langtangen, "Computational Partial Differential Equations Numerical Methods and Diffpack Programming" Springer Verlag, 2003. (Development of FEM programs; using numerical C++ library Diffpack)

S.C. Brenner and L.R. Scott, "The mathematical theory of Finite Element Methods", Springer Verlag, 1994. (Mathematical; elliptic problems, mixed methods,..)

A. Logg, Automating the finite element method.
after the written exam.

MSc projects

You may be interested in a MSc project in Scientific Computing or Numerical Analysis at the School of Computer Science and Communication (CSC). If so, get in touch with course administration, or with any of the NA staff. If you are more interested in Computer Science, get in touch with e.g. Mikael Goldmann.

Preliminary Schedule

pdf here
Sidansvarig: Jesper Oppelstrup <jespero@csc.kth.se>
Senast ändrad 30 augusti 2007
Tekniskt stöd: <webmaster@csc.kth.se>
Copyright © Sidansvarig: Jesper Oppelstrup <jespero@csc.kth.se>
Uppdaterad 2008-04-01