The Finite Element Method
Information for fem08
The goal of this course is to give basic knowledge of the theory 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, discretization error estimates and
algorithms for adaptively refining the mesh (see the FEniCS gallery and the Body and Soul
gallery). The practical part deals with computer implementation:
assembly of element matrices, numerical integration, etc.
Project course continuation
A natural continuation of the finite element course is the
Project
Course in Scientific computing (DN2295), given in period 2 2008. There
you can choose or come up with a project which goes more in depth into
a topic or application. You will receive supervision from members of
our research group (Johan Jansson,
Johan Hoffman, ...).
News
- 081204:
-
The date and place for the re-exam have been set to 2009-01-12
13:15-18:15 in room 4523, floor 5, Osquarsbacken 2. Please email me to
register for the exam. The re-exam will consist of a new chance for
the written examination, you can also submit reports for the modules
in December 2008-January 2009 to me.
- 081105:
-
Grades have been submitted to the student expedition. The grades are
set by a sum of modules points (maximum 30p, where you need at least 14p
to pass) and written exam points (maximum 30p, where you need at least
14p to pass) with at least a pass necessary on each part. This is the
grading scale (maximum 60p):
FX: 24p E: 27p D: 34p C: 41p B: 47p A: 54p
Written exam paper 2008-10-21
and solutions 2008-10-21.
Please take some time to give some feedback in the course evaluation form (see below).
Thanks for making the course interesting and good luck in the future.
- 081027:
-
Home
page for project course now up. Mail me if you want to take the
course and haven't talked to me about it yet. First meeting is wednesday 2008-10-29 at 10:15 in 4523.
- 081020:
-
The deadline for modules 6-9 has been extended until October 24 due to
the lab computer kd0 being unusable over the weekend. Note for the
exam: there are no aids allowed.
- 081020:
-
The kd0 computer seems to have had some trouble over the weekend, I'm aware of
this and will extend the module deadline for those who need it.
- 081010:
-
Updated examination question for module 9 (clarification).
- 081009:
-
Modules 8 and 9 have been updated (completed). See lecture notes for
lecture 9 below for repetition/overview and information in preparation
for the written part of the examination.
- 081009:
-
The first batch of modules have been graded and can be picked up in
the lab on friday or from Murtazo's office.
- 081009:
-
All examination questions in the remaining modules are now up.
- 081007:
-
Typical examination questions in preparation for the written exam.
- 081003:
-
Note correction in module 5 for the velocity beta. It should be a
counterclockwise rotating velocity field. The remaining modules will
be up before monday. The question in module 6 will deal with
implementation of adaptive mesh refinement with regard to an error
indicator based on the residual.
- 080929:
-
Put up "office hours" at tuesdays 15-16 in room 1517. Take advantage
of these extra sessions if you feel you're falling behind.
- 080925:
-
Last question is up for module 5 (apologies for delay). Remember deadline at
october 3 for modules 4-5.
- 080924:
-
Updated error estimation module (number 5).
- 080917:
-
Uploaded notes for lecture 5 and 6. Updated module pages with FEniCS instructions.
- 080909:
-
If you can't login to our computers, go to the reception of the system group for CSC and get an account.
- 080905:
-
Examination questions in the first three course modules are now available, with deadline 19 September.
- 080902:
-
Uploaded notes for lecture 2.
- 080901:
-
Uploaded notes for lecture 1.
Course modules are now accessible.
- 080901:
-
Course starts Tuesday September 2, 8-10, in E3.
Registration
To register for this course you need to
sign up electronically.
Teachers
- Coordinator and lecturer is
Johan Jansson; email:
jjan@csc.kth.se
- Exercise assistant is Niclas Jansson; email:
njansson@csc.kth.se
- Lab assistant is Murtazo Nazarov; email:
murtazo@csc.kth.se
Office Hours
- Johan Jansson (1517): Tuesdays 15.00-16.00
Meet me in my office if you feel you're falling behind, then we can go
through the parts which are not clear.
Examination
The examination consists of submissions of written reports and
software for the course modules ( FEM08
modules at www.icarusmath.com) and a written exam.
- (1) Written exam: Tuesday October 21, 14-19. Typical examination questions.
- (2) Reports for modules 1-3 are due September 19, modules 4-5 October 3, the rest of the modules October 20. Give your answers with source code and possible figures in a PDF. Mail the PDF to me (jjan@csc.kth.se) with the text "module 1-3" in the title.
The modules should be carried out individually or in groups of two.
Course evaluation form
Please fill out the course evaluation form after the written exam.
The following message means that your submitted form has been received:
Din utvärdering har tagits emot. Tack för hjälpen!
Literature
Course book (CDE)
"K. Eriksson, D. Estep, P. Hansbo, C. Johnson: Computational Differential Equations",
Studentlitteratur, ISBN ISBN 91-44-49311-8. Price: ? kr at
kårens bokhandel.
Hints and solutions to some of the problems in the book.
Useful inequalities.
More books in the same series.
Project
Extra material
- FEM course from 2006 (has older lecture notes, etc.)
- Computer Sessions (older Octave/Matlab educational version of FEniCS)
- Puffin
- 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,...)
- FEM notes from a numerical analysis course in Uppsala
(summarizes some parts of the book)
- Laplacian models (AMBS) (some PDE applications)
- Robin boundary conditions
- Robin boundary conditions in 2D
- 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 excercises:
- 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
P. Hansbo, Beyond the elements of finite elements. (Solid mechanics, general
algorithms for non-linear problems)
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.
D. Estep, A short course on duality, adjoint operators, Green's functions, and a posteriori error analysis.
Navier-Stokes: Quick and Easy
Compressible Flow (p. 37- for compressible Euler in 2d/3d)
MSc projects
You may be interested in a MSc project at the School of Computer Science and Communication (CSC).
MSc projects at CSC are avaliable here.
Schedule
The lecture/exercise/lab schedule
Preliminary weekly plan
Week 1
- Lecture 1:
-
Course overview, differential equations, Poisson 1D, boundary conditions, weak formulation, polynomial approximation, interpolation, L2 projection, Galerkin method, piecewise polynomials 1D
(CDE 1-4,6,8.1).
(modules 1-3).
- Lecture 2:
-
Poisson 2D, assembly algorithm, FEM mesh, piecewise polynomials 2D,
quadrature, affine mapping
(CDE 5.5,(7),13,14.1-14.2,14.4,15.1).
(modules 3-4)
Week 2
- Lecture 3:
- Boundary conditions, FEniCS
(CDE 8.1.5, 15.1,15.3,15,4, Robin boundary conditions in
1D and
2D).
- Lecture 4:
- error estimation, adaptivity
Week 3
- Lecture 5:
- error estimation 2D, mesh operations
(CDE 5,8.2-8.6,14.2,15.2-15.3).
- Lecture 6:
- Initial value problem, heat equation, space-time FEM, stability
(CDE 9.1-9.2,16,17).
Week 4
- Lecture 7 (see module 8 for "lecture notes"):
- Convection-diffusion-reaction equation, stabilization, wave equation
Problem 18.6
(CDE 18,19).
Week 5
- Lecture 8 (see modules 9 for "lecture notes"):
- Uniqueness and existence for elliptic PDE, Lax-Milgram
(CDE 21,12).
Week 6
- Lecture 9:
- ALE, Navier-Stokes, overview/repetition
(CDE ).
Week 7
Work on modules/projects.
Week 8
Exam.
Sidansvarig: Johan Jansson <jjan@csc.kth.se>
Senast ändrad 10 oktober 2008
Tekniskt stöd: <webmaster@csc.kth.se>
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