Syllabus for Advanced Numerical Methods
Avancerade numeriska metoder
A revised version of the syllabus is available.
- 10 credits
- Course code: 1TD050
- Education cycle: Second cycle
Main field(s) of study and in-depth level:
Computational Science A1F,
Computer Science A1F,
Explanation of codes
The code indicates the education cycle and in-depth level of the course in relation to other courses within the same main field of study according to the requirements for general degrees:
- G1N: has only upper-secondary level entry requirements
- G1F: has less than 60 credits in first-cycle course/s as entry requirements
- G1E: contains specially designed degree project for Higher Education Diploma
- G2F: has at least 60 credits in first-cycle course/s as entry requirements
- G2E: has at least 60 credits in first-cycle course/s as entry requirements, contains degree project for Bachelor of Arts/Bachelor of Science
- GXX: in-depth level of the course cannot be classified
- A1N: has only first-cycle course/s as entry requirements
- A1F: has second-cycle course/s as entry requirements
- A1E: contains degree project for Master of Arts/Master of Science (60 credits)
- A2E: contains degree project for Master of Arts/Master of Science (120 credits)
- AXX: in-depth level of the course cannot be classified
- Grading system: Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
- Established: 2016-03-10
- Established by: The Faculty Board of Science and Technology
- Applies from: Autumn 2015
120 credits in science/engineering including 45 credits in mathematics, where linear algebra, vector calculus, transform theory (Fourier analysis) must be covered. Scientific Computing III. Applied Finite Element Methods or Finite Element Methods.
- Responsible department: Department of Information Technology
To pass the course the student shall be able to
- review and apply fundamental theory for mathematical modelling of partial differential equations;
- analyse finite difference and finite element approximations of systems of partial differential equations;
- review and describe application areas where different types of finite element and finite differences are used;
- choose, formulate and implement appropriate numerical methods for solving science and engineering problems that are formulated as partial differential equations;
- interpret, analyse and evaluate results from numerical computations;
- use common software to solve application problems formulated as more complicated partial differential equations, such as linear elasticity and transport problems.
The content is built up around a design problem. It focuses on keywords such as consistency, convergence, stability, existence, uniqueness and efficiency.
The course covers the Fourier method, Energy method, normed vector spaces, bilinear forms, Lp - and Sobolev spaces, weak derivatives, elliptic boundary value problems, hyperbolic and parabolic time-dependent initial value problems, linearisation for nonlinear problems, interpolants and finite elements, higher order methods and elements, stabilisation, a priori and posteriori error bounds.
Analyse linear systems of partial differential equations, analyse finite difference and finite element methods of systems of nonlinear partial differential equations. The methodology in finite difference and finite element methods (Lax-Richtmeyer, Lax-Milgram) and applying explicit and implicit time discretisation methods.
Lectures, problem solving sessions and assignments.
Written final exam (6 credits) and assignments (4 credits).
- Latest syllabus (applies from Autumn 2023)
- Previous syllabus (applies from Spring 2019)
- Previous syllabus (applies from Spring 2017)
- Previous syllabus (applies from Autumn 2015)
Applies from: Autumn 2015
Some titles may be available electronically through the University library.
Larson, M. G.;
A first course in finite elements: lecture notes
Department of Mathematics, Umeå university, 2010