SMN6203 PDE and the Finite Element Method - 7.5 stp

The course will provide an introduction to some important analytical and numerical methods for solving partial differential equations. It will also provide an introduction to Sobolev-space and variation formulations with applications to the finite element method.

Classical theory of partial differential equations, Sobolev-space and variation formulations. Numerical methods for solving partial differentiallikninger are also considered (difference methods and finite element method). Large parts of the course will be conducted using video lectures that students can see and hear by using the PC. For more information, see the course homepage which you can access through Its Learning when you are registered for the course.

A relevant undergraduate bachelor Engineering programme with minimum 30 credits Mathematics/statistics topics

Prerequisite(s)

Based on the courses Linear Algebra and Numerical Methods

Application code: 9371

Knowledge

After completing the course, the student:

• has some knowledge within the academic field of mathematics, physics and engineering and specialized insight in a limited area within the field of master of science (K1)
• can apply knowledge to some new areas within the academic field of numerical and analytical calculations, computations, materials, systematic design process, computational methods, engineering design (K3)

Skills

After completing the course, the candidate:

• can analyze and deal critically with information and use them to structure and formulate scholarly arguments (S1)
• can carry out an independent, limited research or development project under supervision and in accordance with applicable norms for research ethics (S4)

General competence

After completing the course, the candidate:

• can analyze some relevant academic, professional and research ethical problems (GC1)
• can communicate extensive independent work and masters language and some terminology of the academic field of master of science (GC3)

Large parts of the course will be conducted using video lectures that students can see and hear by using the PC. For more information, see the course homepage which you can access through Its Learning when you are registered for the course.

In addition, individual supervision and regular lectures which include review of the assignments are made.

Mandatory tasks:

At the start of the written exam, the students bring with them a predefined report in two paper copies. 

This report can be used by the students during the written exam, and the report will count as part of the exam (there will be no separate grade for the report). The whole material, also the report, has to be delivered at the end of the exam.

Examination and report will form the basis of the overall assessment.           

Exam:

3 hour written exam

Access to the continuation exam, if it is held, requires that the professor must approve the report within 1 month after the regular examination is held. Remember to take care of the report, since it has to be delivered on a possible continuation exam.  Grading will be done by using A-F grading scale, F is Fail. There will be no separate grade for the report.

The date for the exam can be changed. The final date will be announced at your faculty early in May and early in November.

* E.Kreyszig: Advanced engineering mathematics, Latest Edition, John Wiley and Sons, Inc., New York. * D. Lukkassen: An introduction to Sobolev spaces for engineering students, Kompendium, HiN 2004.

 *lectures, notes,  distributed material and the project tasks/reports

Additional literature

*Johnson, Claes, Numerical Solutions of Partial Differential Equations by FEM, Studentlitteratur, rev. 1994, published 1987, ISBN: 9144252412.

*K. Eriksson, D. Estep, P. Hansbo, C. Johnson, Computational Differential Equations, Cambridge University Press and Studentlitteratur, 1996, ISBN 91-44-49311-8