Course: Finite Element Method

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Course title Finite Element Method
Course code KMA/MKPA
Organizational form of instruction Lecture + Exercise
Level of course Master
Year of study not specified
Semester Winter
Number of ECTS credits 3
Language of instruction Czech
Status of course Compulsory-optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Netuka Horymír, RNDr. Ph.D.
  • Ligurský Tomáš, RNDr. Ph.D.
Course content
1. History of development and value of the finite element method (FEM). 2. Example: The beam bending problem. 3. Linear elasticity problem. 4. The basic idea of the FEM as a variational method. 5. Triangulation. 6. Finite elements and their examples. 7. Finite element spaces. 8. Convergence of the FEM. 9. Quadrature formulae used in FEM. 10. Effect of numerical integration on the finite element solution. 11. Algorithm of the FEM: Assembling techniques for the stiffness matrix and methods of solving the finite element systems of equations. 12. Solution of parabolic problems: Weak semi-discrete formulation, the Faedo-Galerkin method. 13. Introduction to finite element approximation of nonlinear problems.

Learning activities and teaching methods
Lecture, Monologic Lecture(Interpretation, Training)
  • Attendace - 39 hours per semester
  • Homework for Teaching - 15 hours per semester
  • Semestral Work - 35 hours per semester
Learning outcomes
Understand and be able to use the most widespread computational method for boundary value problems.
Knowledge Gain knowledge about well-known method for solution of boundary value problems.
Prerequisites
Student has to pass the course Variational methods (KMA/VM). Standard knowledge from numerical mathematics.
KMA/VM

Assessment methods and criteria
Oral exam, Seminar Work

Credit: the student has to compute a given example.
Recommended literature
  • J. Haslinger. (1980). Metoda konečných prvků pro řešení eliptických rovnic a nerovnic. MFF UK, Praha.
  • J. N. Reddy. (1993). An Introduction to the Finite Element Method, 2nd edition. McGraw-Hill New York.
  • M. Křížek, P. Neittaanmaki. (1990). Finite element approximation of variational problems and applications. Longman.
  • P. Ciarlet. (1978). The Finite Element Method for Elliptic Problems. North-Holland Amsterdam.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester