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 semidiscrete formulation, the FaedoGalerkin 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 wellknown 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. McGrawHill 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. NorthHolland Amsterdam.
