A second course on computational methods focusing on the finite element method (FEM) and partial differential equations.

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Content and learning outcomes

Course contents

For elliptical and parabolic differential equations, and briefly for hyperbolic problems, the course addresses how to rewrite the problem in a form suitable for treatment with the finite element method, select appropriate mesh, element, variational formulation and how to implement the finite element method using both self-written code and existing routines. The theoretical part of the course deals with deriving error estimates and stability results given scalar linear partial differential equations.

The course deals with, for example: the weak formulation, mesh generation, function spaces, different element types, the Lax-Milgram theorem, interpolation, a priori error estimates, a posteriori error estimates, adaptivity, stability, accuracy, computational cost and discretization.

Intended learning outcomes

An overall goal of the course is to provide the student with both theoretical and practical skills to make reliable and efficient computations using the finite element method for models, described as Partial Differential Equations (PDEs), treated in the course as described in the course content.

After completing the course, the student shall be able to

• given a PDE rewrite it in a form suitable for treatment with the finite element method.
• describe key concepts and basic ideas of the finite element method and be able to use these concepts and ideas to describe advantages and limitations of the finite element methods included in the course.
• describe, apply, and implement the finite element methods included in the course.
• derive error estimates for the finite element solution, stability of the finite element method and well-posedness of the given PDE using theorems and analytical procedures included in the course.

Course Disposition

No information inserted

Literature and preparations

Specific prerequisites

• Completed basic course in numerical analysis (SF1550 or SF1544 or equivalent) and
• Completed basic course in computer science (DD1331 or DD1320 or equivalent)

Recommended prerequisites

SF2520 Applied Numerical Methods (or corresponding), can be read in parallel.

Equipment

No information inserted

Literature

To be announced at least 4 weeks before course start at course web page. Previous year:
K. Eriksson, D. Estep, P. Hansbo, C. Johnson: Computational Differential Equations.
Studentlitteratur, ISBN 91-44-49311-8

Examination and completion

If the course is discontinued, students may request to be examined during the following two academic years.

A, B, C, D, E, FX, F

Examination

• LAB2 - Laboratory Work, 4,5 hp, betygsskala: P, F
• TEN2 - Written Examination, 3,0 hp, betygsskala: A, B, C, D, E, FX, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

Opportunity to complete the requirements via supplementary examination

No information inserted

Opportunity to raise an approved grade via renewed examination

No information inserted

Ethical approach

• All members of a group are responsible for the group's work.
• In any assessment, every student shall honestly disclose any help received and sources used.
• In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.

Further information

Course web

Further information about the course can be found on the Course web at the link below. Information on the Course web will later be moved to this site.

Course web SF2561

SCI/Mathematics

Main field of study

Mathematics, Technology

Second cycle