Syllabus for Finite Element Methods

Finita elementmetoder

Syllabus

  • 5 credits
  • Course code: 1TD253
  • Education cycle: Second cycle
  • Main field(s) of study and in-depth level: Computer Science A1F, Technology A1F, Computational 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:

    First cycle
    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.

    Second cycle
    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: 2010-03-18
  • Established by: The Faculty Board of Science and Technology
  • Revised: 2012-04-23
  • Revised by: The Faculty Board of Science and Technology
  • Applies from: week 14, 2014
  • Entry requirements: 120 credits of which at least 45 credits in mathematics, Computer Programming I and Scientific computing III or the equivalent.
  • Responsible department: Department of Information Technology

Learning outcomes

To pass the course the student shall be able to

  • explain fundamental concepts in mathematical modelling with partial differential equation, and fundamental properties for elliptic, parabolic and hyperbolic equations;
  • formulate and with a computer solve second order elliptic boundary value problems in one spatial dimension using the finite element method.
  • formulate and with a computer solve second order elliptic boundary value problems in two spatial dimensions with Dirichlet, Neumann, and Robin boundary conditions, using the finite element method.
  • derive a priori and a posteriori error bounds for elliptic equations in one and two spatial dimensions, and be able to use these error bounds to construct adaptive algorithms for local mesh refinement.
  • solve parabolic and hyperbolic partial differential equations using the finite element method in space and finite differences in time, and to compare different time stepping algorithms and choose appropriate algorithms for the problem at hand.
  • use finite element software to solve more complicated problems, such as coupled systems of equations.
  • evaluate different techniques for solving problems and be able to motivate when to use existing software and when to write new code.

Content

Discrete function spaces in one and two spatial dimensions. Variational formulation of elliptic boundary value problems. Finite element methods in one and two spatial dimensions. Error bounds for the finite element approximation of elliptic problems. Adaptive mesh refinement. Time dependent problems where finite elements are used in space and finite differences in time. Use existing FEM-software, such as Comsol-Multiphysics.

Instruction

Lectures, laboratory work, compulsory assignments. Guest lecture.

Assessment

Written examination (3 credits) and compulsory assignments (2 credits).

Reading list

Reading list

Applies from: week 14, 2014

  • Eriksson, Kenneth Computational differential equations

    Lund: Studentlitteratur, 1996

    Find in the library